We aim to design an analog-only beamforming scheme for downlink multi-user mm-wave systems to optimize the beamforming gain and the inter-user interference at the same time. Traditional analog beamforming schemes, such as the beam selection method, use the array response vector corresponding to the strongest path of the channel to generate a beam pointing to the user. In multi-user systems, such schemes will lead to large inter-user interference, especially when the users are closely located. In this paper, we formulate a multi-objective problem to strike a balance between the beamforming gain and the inter-user interference. To solve the problem, we first use the weighted-sum method to transform the multi-objective problem into a single-objective problem. Then, we use the semi-definite programing technique to make the analog beamforming with constant-magnitude constraints tractable. Furthermore, to alleviate the effects of the channel estimation and feedback quantization errors, we design a robust beamforming scheme to provide robustness against imperfect channel information. We first develop a channel error model for the scattering clustered channel model, which can serve as a general channel error model for the mm-wave channels. Then, we formulate a multi-objective problem using the stochastic approach to suppress the interference and enhance the beamforming gain at the same time. The simulation results show that our proposed non-robust multi-user analog beamformer outperforms the traditional analog beamforming method when the SNR is high and our proposed robust beamformer can provide up to 109% improvement in the sum-rate compared with the beam selection method.