Owing to the distributed features and flexibility, carrier sense multiple access with collision avoidance (CSMA/CA) mechanisms have been widely adopted in wireless networks. Considering energy consumption, we devote to exploring an energy efficient carrier sense multiple access with collision avoidance (EE-CSMA/CA) mechanism. The access delay and delay jitter are two of most important quality of service (QoS) metrics. EE-CSMA/CA inevitably experiences the tortures bred from its delay and delay jitter performance, because its frame structure with inactive period brings delay. In this paper, we aim to analyze the access delay and delay jitter of packets for the CSMA/CA with inactive period under the unsaturated conditions. Based on the Markov theory, we model the mechanism of EE-CSMA/CA as a four-dimensional Markov chain, and the fourth variable of Markov chain differentiates the active period and the inactive period of EE-CSMA/CA. Then, deriving in probability generation domain, we get the probability distribution of service time and obtain the access delay. Finally, the queue in a node is decoupled, and two queues with different states of empty and non-empty are configured logically, which helps to enable the complex analysis of delay jitter. Based on the whole probability analysis, the probability distribution of delay jitter is obtained. We show that the active ratio (active time over whole frame time) affects the access delay and delay jitter. When the active ratio is constant, the duration of active period has less effect on the access delay while it deteriorates delay jitter performance.