We study the waiting time distribution of giant pulses from the Crab pulsar observed with the Nanshan 26-m radio telescope at a center frequency of 1556MHz with 512 MHz bandwidth. The observations were performed over a duration of 12.6 hours with 32μs sampling interval. Our analysis has led to the detection of 2097 giant pulses above a threshold of 10 sigma, with flux density $>$ 100Jy. The occurrence rate of giant pulses is characterized by a highly intermittent giant pulse productivity in short clusters with high rates, separated by relatively long quiescent intervals with low occurrence rates, especially for the giant pulses associated with the interpulse emission. The distribution of waiting times between two subsequent giant pulses displays a power-law tail and can be modeled with a non-stationary Poisson process, which indicates that giant pulses are independent and random events. Distinct waiting time distributions between giant pulses in the main pulse and interpulse phases are presented, which implies that the giant pulse emission mechanisms maybe different in the opposite magnetic poles. The ramification for our understanding of the radio emission mechanisms is discussed.