Dead-time has a significant influence on the detection efficiency and range performance of a photon-counting laser radar system with a Geiger-mode avalanche photodiode. In this paper, a rapid universal recursive model of the detection probability of discrete time under various dead-times is proposed, which is verified with controlled parameters. Our model has the advantage of fast computing speed and unifies multi-trigger, single-trigger, and zero-dead-time models. The computing speed is 1 to 2 orders of magnitude faster than Gatt's and Zhao's models under a short dead-time condition, with relative errors less than 0.001 and 10-14, respectively. Subsequently, the detection efficiency and range bias and precision with various dead-times are theoretically calculated and Monte Carlo simulated with different parameters. On the one hand, dead-time shorter than the end time of the target achieves better detection efficiency; however, this results in worse range performance. On the other hand, dead-time longer than the end time of the target maintains the detection efficiency at a low level but provides a better range performance. We discover that noise is the key reason for the periodic fluctuation of the detection efficiency and range performance versus different dead-times and the local optimum values of fluctuations occur when the dead-time is a few nanoseconds shorter or longer than 1, 1/2, 1/3, or even 1/4 of the end time of the target; further, this phenomenon becomes more evident when noise increases. Moreover, weaker noise level is crucial to the detection efficiency, and narrow pulse width and nearer target position in the range gate are important factors to improve precision.