In wireless energy harvesting communication networks, a user receives wireless energy released by an ambient or dedicated energy source, and uses that energy for delay constrained data transmission. However, such data transmission can be susceptible to a jamming attack from a nearby attacker also harvesting from the wireless energy source. In this paper, we consider such a scenario and present performance analysis. In particular, we develop an analytical model for the network based on a Markov chain to obtain various performance measures for the user including throughput and delay distribution. The performance evaluation shows some interesting results. For example, under the jamming attack, there is a maximum achievable throughput of the user. We also validate the analytical model using simulation.