In recent years, the interest of industry towards condition-based maintenance, substituting traditional time-based maintenance, is growing. Indeed, condition-based maintenance can increase the system uptime with a consequent economic advantage. In this paper, a solution to detect the health state of a variable displacement axial-piston pump based on vibration signals is proposed. The pump was tested on the test bench in different operating points, both in healthy and faulty conditions, the latter obtained by assembling damaged components in the pump. The vibration signals were acquired and exploited to extract features for fault identification. After the extraction, the obtained features were reduced to decrease the computational effort and used to train different types of classifiers. The classification algorithm that presents the greater accuracy with reduced features was identified. The analysis has also showed that using the time sampling raw signal, a satisfying accuracy could be obtained, which will permit onboard implementation. Results have shown the capability of the algorithm to identify which fault occurred in the system (fault identification) for each working condition. In future works, the classification algorithm will be implemented onboard to validate its effectiveness for the online identification of the typical incipient faults in axial-piston pumps.