In this paper, under saturated traffic condition in a single-hop wireless sensor network, we present an analytic model that evaluates the performance of asynchronous MAC protocol which uses a preamble technique. Our model considers the impact of several important factors such as sleep cycle, the backoff mechanism and the number of contending nodes. After obtaining the cumulative backoff time of a sending node and expected delay of a receiving node, an iterative algorithm is presented for calculating the performance measures such as expected energy consumption usage per packet and latency. Simulation results show that the proposed analytic model can accurately estimate the performance measures under saturated traffic conditions.