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The reaction-diffusion system is naturally used in chemistry to represent substances reacting and diffusing over the spatial domain. Its solution illustrates the underlying process of a chemical reaction and displays diverse spatial patterns of the substances. Numerical methods like finite element method (FEM) are widely used to derive the approximate solution for the reaction-diffusion system. However, these methods require long computation time and huge computation resources when the system becomes complex. In this paper, we study the physics of a two-dimensional one-component reaction-diffusion system by using machine learning. An encoder-decoder based convolutional neural network (CNN) is designed and trained to directly predict the concentration distribution, bypassing the expensive FEM calculation process. Different simulation parameters, boundary conditions, geometry configurations and time are considered as the input features of the proposed learning model. In particular, the trained CNN model manages to learn the time-dependent behaviour of the reaction-diffusion system through the input time feature. Thus, the model is capable of providing concentration prediction at certain time directly with high test accuracy (mean relative error <3.04%) and 300 times faster than the traditional FEM. Our CNN-based learning model provides a rapid and accurate tool for predicting the concentration distribution of the reaction-diffusion system.