In this paper, we propose a robust analog-only beamforming scheme for the downlink multi-user systems, which not only suppresses the interference and enhances the beamform- ing gain, but also provides robustness against imperfect channel state information (CSI). We strike a balance between the average beamforming gain and the inter-user interference by formulating a multi-objective problem. A probabilistic objective of leakage interference power is formulated to alleviate the effects of the channel estimation and feedback quantization errors. To solve the problem, we first use the sum-weighted method to transform the multi-objective problem into a single-objective problem. Then, we use the semi-definite programing technique to make the constant- magnitude constraints of the analog beamforming tractable. Simulation results show that our proposed robust beamformer can provide up to 120% improvement in the sum-rate compared to the beam selection method.