As a stealthy cyber attack, false data injection attack (FDIA) can bypass the traditional bad data detection module to threaten the security and economics of smart grids. The uncertainties of renewable energy, power loads, and network parameters perturbations can cause a lot of noise and errors in the measurement data. Therefore, this paper proposes an FDIA detection method combining the principal component analysis (PCA) and convolutional neural network (CNN) to improve the detection accuracy and speed. PCA achieves dimensionality and noise reductions of the high-dimensional characteristic measure-ment data and retains the original data's complete information. Inspired by deep learning research results, CNN is used as a classifier to perform translation-invariant classification on the dimensionality-reduced quantitative measurement data. Some simulation results on IEEE bus systems have been presented to show that the detection method proposed has high accuracy compared with other traditional strategies.