The performance of window-based PN acquisition algorithm is fully analyzed by Markov chain acquisition model on the assumption of direct sequence code division multiple access forward link. The algorithm with a moderate window size has shorter acquisition time than the immediate verification algorithm has - especially in low Ec/No. This results from the fact that the window-based algorithm, which verifies only one code phase that has maximum correlation output, consumes an additional penalty time in each window even in the condition of frequent false alarms. As the mean acquisition time varies with the window size, we may have the code acquisition fast with the proper window size according to Ec/No.