Matrix-factorization based collaborative filtering is an efficient approach to the problem of user-side quality-of-service (QoS) prediction. In this work, we focus on building a matrix-factorization-based collaborative filtering model for QoS prediction under a non-negativity constraint. The motivation is that since QoS data such as response time, cost and throughput, are all positive, a non-negative model can better demonstrate their characteristics. By investigating a non-negative training process relying on each involved feature, we invent a non-negative latent factor model to deal with the sparse QoS matrix subject to the non-negativity constraint. We subsequently introduce Tikhonov regularization into it to obtain the regularized non-negative latent factor model. Their efficiency is proven by the experimental results on a large industrial dataset.