Arc faults in an aircraft’s power distribution system (PDS) often leads to cable and equipment damage, which seriously threatens the personal safety of the passengers and pilots. An accurate and real-time arc fault detection method is needed for the Solid-State Power Controller (SSPC), which is a key protection equipment in a PDS. In this paper, a new arc detection method is proposed based on the improved LeNet5 Convolutional Neural Network (CNN) model after a Time−Frequency Analysis (TFA) of the DC currents was obtained, which makes the arc detection more real-time. The CNN is proposed to detect the DC arc fault for its advantage in recognizing more time−frequency joint details in the signals; the new structure also combines the adaptive and multidimensional advantages of the TFA and image intelligent recognition. It is confirmed by experimental data that the combined TFA−CNN can distinguish arc faults accurately when the whole training database has been repeatedly trained 3 to 5 times. For the TFA, two kinds of methods were compared, the Short-Time Fourier Transform (STFT) and Discrete Wavelet Transform (DWT). The results show that DWT is more suitable for DC arc fault detection. The experimental results demonstrated the effectiveness of the proposed method.