Modeling the lead-time demand for the multiple slow-moving inventory items in the case when the available requests history is very short is a challenge for inventory management. The classical forecasting technique, which is based on the aggregation of the stock keeping units to overcome the mentioned historical data peculiarity, is known to lead to very poor performance in many cases important for industrial applications. An alternative approach to the demand forecasting for the considered problem is based on the Bayesian paradigm, when the initially developed population-averaged demand probability distribution is modified for each item using its specific requests history. This paper follows this approach and presents a new model, which relies on the beta distribution as a prior for the request probability, and allows to account for disparity in variance of demand between different stock keeping units. To estimate the model parameters, a special computationally effective technique based on the generalized method of moments is developed. Simulation results indicate the superiority of the proposed model over the known ones, while the computational burden does not increase.