Device-free gait recognition is a promising technique which could provide insensible identification for smart applications. It leverages the unique influence of the target's gait on surrounding wireless signals to achieve identity recognition in a contact-free and device-free manner. Existing device-free gait recognition methods could achieve good accuracy when a target walks along a predetermined path. However, the accuracy will drop dramatically when a target walks along an arbitrary path. This is due to the fact that different paths will exert different influence on the wireless signals. In order to address this issue, we develop a path-independent device-free gait recognition system, which can recognize the identity of a person no matter what path he/she walks. Specifically, we propose a novel robust path-independent gait spectrogram construction method, which leverages location information and doppler spectrogram to generate corrective velocity spectrogram so as to approximate the actual velocity spectrogram, and utilizes an energy normalization strategy to eliminate the influence of path on spectrogram energy so as to achieve the independence of the walking path. Based on the path-independent gait spectrogram, we use a convolutional neural network to extract deep features and accomplish the gait recognition task. Experimental results conducted on a 77 GHz mmWave testbed, and achieve the average accuracies of 91% and 87% in the non-radial straight path and curve path, respectively, when 10 targets are trained in the radial path.