Effects of plasma density distributions on self-focusing of intense laser pulses propagating in an underdense cold plasma are investigated, where the laser intensity has a Gaussian distribution and the initial plasma density is cylindrical-symmetrically distributed. An evaluation function is derived to judge which type of plasma density distribution is more beneficial for the occurrence of self-focusing. Through analyzing and calculating the evaluation function, it is found that for a given laser field and with fixed initial plasma density along the central axis, which coincides with the axis of the laser beam, increasing plasma density with the distance from the axis favors self-focusing. Furthermore, the greater the density gradient, the more favorable. It is also found that the combined action of both relativistic and ponderomotive effects is of more advantage to self-focusing than that of relativistic effect alone. Numerical simulation confirms that the evaluation function is capable of accurately predicting the favorable role of plasma density distribution in producing laser self-focusing.