Developments in radio detection and ranging (radar) technology have made hand gesture recognition feasible. In heat map-based gesture recognition, feature images have a large size and require complex neural networks to extract information. Machine learning methods typically require large amounts of data and collecting hand gestures with radar is time- and energy-consuming. Therefore, a low computational complexity algorithm for hand gesture recognition based on a frequency-modulated continuous-wave (FMCW) radar and a synthetic hand gesture feature generator are proposed. In the low computational complexity algorithm, two-dimensional Fast Fourier Transform is implemented on the radar raw data to generate a range-Doppler matrix. After that, background modelling is applied to separate the dynamic object and the static background. Then a bin with the highest magnitude in the range-Doppler matrix is selected to locate the target and obtain its range and velocity. The bins at this location along the dimension of the antenna can be utilised to calculate the angle of the target using Fourier beam steering. In the synthetic generator, the Blender software is used to generate different hand gestures and trajectories and then the range, velocity and angle of targets are extracted directly from the trajectory. The experimental results demonstrate that the average recognition accuracy of the model on the test set can reach 89.13% when the synthetic data are used as the training set and the real data are used as the test set. This indicates that the generation of synthetic data can make a meaningful contribution in the pre-training phase.