A novel method of predicting the worst-case noise of a power distribution system is proposed in this paper. This method takes into account the effect of the transition time of load currents, and thus allows a more realistic worst-case noise prediction. A dynamic programming algorithm is introduced on the time-domain impulse response of the power distribution system, and a modified Knuth-Yao Quadrangle Inequality Speedup is developed which reduces the time complexity of the algorithm to O(nmlog(n)), where n is the number of discretized current values and m is the number of zeros of the system impulse response. With the algorithm, the worst-case noise behavior of the power distribution system is investigated with respect to the transition time. Experimental results show that assuming a zero current transition time leads to an overly pessimistic worst-case noise prediction.