Recently, robust minimum variance (MV) beamforming which optimizes the worst-case performance has been proposed in [1], [2]. The worst-case approach, however, might be overly conservative in practical applications. In this paper, we propose a more flexible approach that formulates the robust adaptive beamforming problem as a probability-constrained optimization problem with homogeneous quadratic cost function. Unlike the general probability-constrained problem which can be nonconvex and NP-hard, our problem can be reformulated as a convex nonlinear programming (NLP) problem, and efficiently solved using interiorpoint methods. Simulation results show an improved robustness of the proposed beamformer as compared to the existing state-of-the-art robust adaptive beamforming techniques.