Based on the property of the non-instantaneous deteriorating products, a multi-item joint replenishment model is developed under deterioration-time-dependent demand, aiming to minimize the average total cost. Joint replenishment problem is NP-hard, in particular, deterioration increases the complexity of the problem further. In response to this difficulty, the truncated Taylor series expansion is used to simplify the exponential parts of the objective function and a bounds-based heuristic algorithm is developed to solve the proposed model. Finally, sensitivity analysis of key parameters is conducted, which provides useful management suggestions in the implementation of joint replenishment for the retailers of non-instantaneous deteriorating products.