We report critical current density (J(c)) behaviors of the Bi1.7Pb0.3-xGdxSr2Ca3Cu4-O12+y (x = 0.01, 0.1) superconductors prepared by melt-quenching method and annealed in different time intervals at 840 C. The effects of annealing times are found to be very important. For example, for the sample B2, the highest value of J(c) is 3.7 x 10(4) A/cm(2) at 9 K. This value is almost 1.5 and 2 times greater than that of the samples B3 and B1, respectively. With increasing annealing time, the 2223 phase increases, thus resulting in a decrease in the insulating phase. For lower annealing times, there are a large number of insulating phases. On the whole, our results indicate that there is an optimum annealing time t to form the 2223 phase, in a time interval of 120 less than or equal to t less than or equal to 192 h. It is clearly seen that. J(c) decreases smoothly with increasing temperature for all the samples studied. At lower temperatures, especially below 30 K, an extremely rapid decrease of J(c) with increasing temperature has been observed. The experimental values also show that between the temperature interval from 9-45 K, J(c) decreases by one order of magnitude. We have also observed that when the Gd-Pb substitution increases, the effective defect density increases, leading to small critical current densities.