Different from conventional passive reconfigurable intelligent surfaces (RISs), incident signals and thermal noise can be amplified at active RISs. By exploiting the amplifying capability of active RISs, noticeable performance improvement can be expected when precise channel state information (CSI) is available. Since obtaining perfect CSI related to an RIS is difficult in practice, a robust transmission design is proposed in this paper to tackle the channel uncertainty issue, which will be more severe for active RIS-aided systems. To account for the worst-case scenario, the minimum achievable rate of each user is derived under a statistical CSI error model. Subsequently, an optimization problem is formulated to maximize the sum of the minimum achievable rate. Since the objective function is non-concave, the formulated problem is transformed into a tractable lower bound maximization problem, which is solved using an alternating optimization method. Numerical results show that the proposed robust design outperforms a baseline scheme that only exploits estimated CSI.