This paper proposes an analytical model of IEEE 802.15.4, which is a standard toward low complexity, low power consumption and low data rate wireless data connectivity. In this paper, we concentrate on the MAC performance of the IEEE 802.15.4 LR-WPAN with non-beacon mode and non-saturated condition in a star topology. Our approach is to model stochastic behavior of one device as a discrete time Markov chain. We propose an analytical model considering only download traffic.We obtain five performance measures : throughput, packet delay, number of backoff, energy consumption and packet loss probability. Our results are used to find optimal number of devices with some constraints on these measures.