In many autonomous mapping tasks, the maps cannot be accurately constructed due to various reasons such as sparse, noisy, and partial sensor measurements. We propose a novel map prediction method built upon the recent success of Low-Rank Matrix Completion. The proposed map prediction is able to achieve both map interpolation and extrapolation on raw poor-quality maps with missing or noisy observations. We validate with extensive simulated experiments that the approach can achieve real-time computation for large maps, and the performance is superior to the state-of-the-art map prediction approach - Bayesian Hilbert Mapping in terms of mapping accuracy and computation time. Then we demonstrate that with the proposed real-time map prediction framework, the coverage convergence rate (per action step) for a set of representative coverage planning methods commonly used for environmental modeling and monitoring tasks can be significantly improved.