We consider a multi-user multiple-input single-output (MISO) communications system which is assisted by a hybrid active-passive reconfigurable intelligent surface (RIS). Unlike conventional passive RISs, hybrid RIS is equipped with a few active elements with the ability to reflect and amplify incident signals to significantly improve the system performance. Towards a fairness-oriented design, we maximize the minimum rate among all users through jointly optimizing the transmit beamforming vectors and RIS reflecting/amplifying coefficients. Combining tools from block coordinate ascent and successive convex approximation, the challenging nonconvex problem is efficiently solved by a low-complexity iterative algorithm. The numerical results show that a hybrid RIS with 4 active elements out of a total of 50 elements with a power budget of -1 dBm offers an improvement of up to 80% to the considered system, while that achieved by a fully passive RIS is only 27%.