This letter considers a slotted Aloha-based wireless network consisting of multiple nodes with energy harvesting capability. Each node tries to transmit data packets with a delivery deadline by using energy intermittently harvested from the environment. The focus of this letter is that under the constraint of energy availability we derive a timely-delivery ratio, which is defined as the ratio between the average number of data packets transmitted successfully within a given delivery deadline and the average number of all data packets generated. We propose a simple and approximate analytical model for deriving the timely-delivery ratio based on an appropriate decoupling approximation. The accuracy of the proposed model is validated by extensive simulations.