Energy efficiency (EE) and delay are two crucial metrics in WPCN. In general, the transmitter always transmits the information in a good channel state to improve EE while it may lead to delay due to waiting for a good channel state. Thus, there exists a tradeoff between EE and delay. In this paper, we investigate the EE and delay tradeoff with considering the time-varying channel and stochastic traffic arrivals. We formulate this problem as a stochastic optimization model, which optimizes the EE subject to both the data queue stability and the harvested energy availability. To solve the formulation, a general and effective algorithm, referred to as EE and delay tradeoff algorithm (EEDTA), is developed by employing the fractional programming method and Lyapunov optimization theory, which does not require any a prior distribution knowledge of channel states and data arrivals. Moreover, the theoretical analysis and simulation results show that the EEDTA achieves an EE-delay tradeoff, which mathematically depicted by [O(1/V), O(V)] with V as a control parameter, and can flexibly strike the tradeoff by simply tuning V. Simulation results verify the theoretical analysis.