The release of IEEE 802.15.4e specification significantly develops IEEE 802.15.4. The most inspiring improvement is the enhancement for medium access control (MAC) sublayer. To study the performance of IEEE 802.15.4e MAC, in this paper we first present an overview of IEEE 802.15.4e and introduce three MAC mechanisms in IEEE 802.15.4e. And the major concern here is the Time Slotted Channel Hopping (TSCH) mode that provides deterministic access and increases network capacity. Then a detailed analytical Markov chain model for TSCH carrier sense multiple access with collision avoidance (CSMA-CA) is presented. Expressions which cover most of the crucial issues in performance analysis such as the packet loss rate, energy consumption, normalized throughput, and average access delay are presented. Finally the performance evaluation for the TSCH mode is given and we make a comprehensive comparison with unslotted CSMA-CA in non-beacon enabled mode of IEEE 802.15.4. It can validate IEEE 802.15.4e network can provide low energy consumption, deterministic access and increase network capacity.