This study proposes a new method of audio coding based on spectral recovery, which can enhance the performance of transform audio coding. An encoder represents spectral information of an input in a time-frequency domain and transmits only a portion of it so that the remaining spectral information can be recovered based on the transmitted information. A decoder recovers the magnitudes of missing spectral information using a convolutional neural network. The signs of missing spectral information are either transmitted or randomly assigned, according to their importance. By combining transmission and recovery of spectral information, the proposed method can enhance the coding performance, compared with conventional transform coding. The subjective performance evaluation shows that, for mono coding at 39.4 kbps, the proposed method provides higher sound quality than the USAC, by an average MUSHRA score of 8.5.