The binary one-dimensional plasma photonic crystal (1DPPC) based on Fibonacci quasiperiodic structure is studied systematically in this paper. We consider the two simplest cases. In one case, the initial sequences F0 and F1 are both of single layer structure. In another case, one initial sequence (F0 or F1) is of a single layer structure, while the other one (F1 or F0) is of a double layer structure. Thus there are ten different kinds of initial sequences in total. The photonic bandgap characteristics of the 1DPPC with these different initial sequences and numbers of period are analyzed. On these bases, a novel structure of one-dimensional plasma photonic crystal (F3)3 with initial sequence of F0=AP, F1=P and F0=PA, F1=P is proposed in this paper to enlarge the omnidirectional photonic bandgap (OPBG). Compared with previously reported structures in the literature, this structure is simple in configuration with fewer layers and materials, and its OPBG width is wide. The influences of the parameters of the plasma material, such as the thickness, plasma frequency and collision frequency, on the OPBG characteristics of this structure are also discussed. The OPBG width increases with the increase of the thickness and plasma frequency of the plasma layer. Compared with the structures in the literature, the change of OPBG width is the fastest for the proposed structure when the parameters are relatively small. And with the same parameters, the OPBG width for the proposed structure is the widest when the parameters are greater than a certain value. The plasma collision frequency has no effect on the OPBG width for all the structures. But the OPBG width for the proposed structure is the widest when this parameter has the same value. The reason why the proposed structure has an optimal OPBG width is explained by analyzing the dispersion properties of the plasma. The real and imaginary part of the dielectric constant of plasma change with frequency significantly only in the low frequency region. Since the imaginary part of dielectric constant is nearly zero when the frequency is larger than 2 GHz, only the dispersion effect of the real part of dielectric constant needs to be considered in the frequency range we investigate. And its value is much greater than that of conventional medium in the same frequency range. This makes the high-reflectance bands of the 1DPPC broader than those in the case of pure photonic interference phenomena with conventional medium. On the other hand, the corresponding highest proportion of plasma layers in the whole quasiperiodic structure can also be used to explain the broadest band gap of (F3)3. These results can provide important theoretical guidance for designing the novel omnidirectional reflectors.