The existing deep learning-based channel estimation algorithms have significantly higher accuracy than traditional algorithms, but they are difficult to meet the real-time communication requirements due to their slow operation and large parameters, and cannot be effectively deployed on mobile terminals. To address these issues, a lightweight channel estimation neural network model ESPCN-net is proposed, which models the channel estimation problem as a super-resolution task of reconstructing a high-resolution image (i.e., the complete channel response) from a low-resolution image (i.e., the channel response at sparse subcarriers). This model abandons the interpolation step in existing neural network models and directly learns the spatial correlation of channel features from pilot signals without interpolation preprocessing to restore high-precision channel state information. Experimental results show that in typical 5G OFDM multipath channel scenarios, compared with SRCNN and ChannelNet, the proposed model improves the computational efficiency by 25.7% and 77.2 times, respectively. In terms of computational complexity, the number of multiply-accumulate operations is only 36.4% of SRCNN and 0.76% of ChannelNet, demonstrating excellent computational efficiency. In terms of parameter scale, although the 47.25×103 parameters of ESPCN-net are more than those of SRCNN, they are far less than those of ChannelNet (682.34×103) and ReCNet (100.45×103).