Flexible pressure sensors play a crucial role in detecting human motion and facilitating human–computer interaction. In this paper, a type of flexible pressure sensor unit with high sensitivity (2.242 kPa−1), fast response time (80 ms), and remarkable stability (1000 cycles) is proposed and fabricated by the multi-walled carbon nanotube (MWCNT)/cotton fabric (CF) material based on a dip-coating method. Six flexible pressure sensor units are integrated into a flexible wristband and made into a wearable and portable wrist sensor with favorable stability. Then, seven wrist gestures (Gesture Group #1), five letter gestures (Gesture Group #2), and eight sign language gestures (Gesture Group #3) are performed by wearing the wrist sensor, and the corresponding time sequence signals of the three gesture groups (#1, #2, and #3) from the wrist sensor are collected, respectively. To efficiently recognize different gestures from the three groups detected by the wrist sensor, a fusion network model combined with a convolutional neural network (CNN) and the bidirectional long short-term memory (BiLSTM) neural network, named CNN-BiLSTM, which has strong robustness and generalization ability, is constructed. The three types of Gesture Groups were recognized based on the CNN-BiLSTM model with accuracies of 99.40%, 95.00%, and 98.44%. Twenty gestures (merged by Group #1, #2, and #3) were recognized with an accuracy of 96.88% to validate the applicability of the wrist sensor based on this model for gesture recognition. The experimental results denote that the CNN-BiLSTM model has very efficient performance in recognizing different gestures collected from the flexible wrist sensor.