High-dimensional and incomplete (HDI) data are commonly encountered in various big data-related applications concerning the complex interactions among numerous nodes, such as the non-negative interactions among numerous nodes. A non-negative latent factor (NLF) model which depends on a single latent factor-dependent, nonnegative and multiplicative update (SLF-NMU) algorithm process excellent representation learning ability to HDI matrix. However, SLF-NMU algorithm updates a latent factor based on the current stochastic gradient only, without the considerations on the past information, making a resultant model suffer from slow convergence. To address this critical issue, this paper proposes an Adaptive PID-incorporated Non-negative Latent Factor (APNLF) model with three-fold ideas: 1) rebuilding the past update increment following the principle of PID controller to incorporate past update information into the learning scheme efficiently; b) designing a PID-increment-based SLF-NMU (PSN) algorithm to accelerate the convergence rate of model; and c) implementing the gain parameters of a PID controller adaptation by a specially designed fuzzy rule. Experiments on two HDI datasets demonstrate that compared with state-of-the-art models, an APNLF model achieves significant advantage in both efficiency and accuracy.