The modification effects of the groups (CH3)2 and (NH2)2 on the oligo phenylene ethynylene (OPE) molecules with single and double S atoms connected to the two electrodes are investigated by the density functional theory and non-equilibrium Green function. The modified OPE molecule is optimized and used to build a two-probe system with Au electrodes. Then the two-probe system is fully relaxed to obtain a stable structure. The electronic transport properties of the two-probe system are also calculated with the non-equilibrium Green function method. The calculation results show that both the modified groups and the bridge atoms can lead to the switch effect, the negative differential resistance behavior, and the rectifying behavior for the two-probe system. When molecules are connected with single S atom at one end, both the (NH2)2-OPE and the (CH3)2-OPE molecules show the rectifying behavior. However, the (NH2)2-OPE also shows a switch effect at larger voltage because there is current when the negative bias is over 1.3 V, while the (CH3)2-OPE molecule demonstrates a complete rectifying behavior because it is hardly conductive in the whole positive bias area. The current of OPE molecule without modification group always increases with the increase of voltage. Therefore, it is only a resistance. These results are different from that of NO2-OPE-NH2 molecule which shows a negative differential resistance behavior. For the case of the molecule connected with S atoms at both ends, the (NH2)2-OPE(S) and (CH3)2-OPE(S) models show negative differential resistance behaviors in the negative bias range. It is found that both (NH2)2-OPE and (CH3)2-OPE molecules demonstrate the negative differential resistance behaviors when they are connected with S atoms bridge at both ends. However, the current of the molecule with one S atom at one end is about two-order magnitude lower than that of the molecule with S atoms at both ends. It is shown that S atom acting as a bridge can significantly affect the characteristic of current-voltage. The mechanisms for the various characteristics of the electronic transport properties are explored by analyzing the projection orbit electron distribution, the transmission spectrum, and the density of states under the different bias voltages. For (NH2)2-OPE molecule with a single S atom at one end in the negative bias range, only the lowest unoccupied molecular orbital (LUMO) can transfer electron with low bias, but both highest occupied molecular orbital (HOMO) and LUMO can be conductive with high bias, which results in the switch effect. In the positive bias range, both HOMO and LUMO cannot be conductive with low bias, while LUMO can be conductive with high bias, which results in the switch behavior. For the case of (NH2)2-OPE molecule with one S atom at each end, only the HOMO can transfer electron in the low bias range, while the LUMO can be conductive at high positive bias, but both HOMO and LUMO cannot be conductive in high negative bias range, which leads to the non-symmetric negative differential resistance effect in the whole bias range. A similar analysis of the difference between HOMO and LUMO can be used to understand the characteristics of the current-voltage of (CH3)2-OPE. Considering the fact that the different modification groups can lead to various current-voltage properties of OPE molecule, the modified OPE molecule is a promising candidate for designing molecule device.