Finger gesture recognition (FGR) plays a crucial role in achieving, for example, artificial limb control and human-computer interaction. Currently, the most common methods of FGR are visual-based, voice-based, and surface electromyography (EMG)-based ones. Among them, surface EMG-based FGR is very popular and successful because surface EMG is a cumulative bioelectric signal from the surface of the skin that can accurately and intuitively represent the force of the fingers. However, existing surface EMG-based methods still cannot fully satisfy the required recognition accuracy for artificial limb control as the lack of high-precision sensor and high-accurate recognition model. To address this issue, this study proposes a novel FGR model that consists of sensing and classification of surface EMG signals (SC-FGR). In the proposed SC-FGR model, wireless sensors with high-precision surface EMG are first developed for acquiring multichannel surface EMG signals from the forearm. Its resolution is 16 Bits, the sampling rate is 2 kHz, the common-mode rejection ratio (CMRR) is less than 70 dB, and the short-circuit noise (SCN) is less than 1.5 μV. In addition, a convolution neural network (CNN)-based classification algorithm is proposed to achieve FGR based on acquired surface EMG signals. The CNN is trained on a spectrum map transformed from the time-domain surface EMG by continuous wavelet transform (CWT). To evaluate the proposed SC-FGR model, we compared it with seven state-of-the-art models. The experimental results demonstrate that SC-FGR achieves 97.5% recognition accuracy on eight kinds of finger gestures with five subjects, which is much higher than that of comparable models.