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In this paper, we consider the utility maximization problem for proportional fairness using capacity with outage. Firstly, we formulate a log utility maximization problem in case of perfect orthogonal channels. With the gradient algorithm of convex optimization problem, we present the implementation algorithm for maximizing utility of capacity with outage. Also, we extend the result to the case with interference due to non-orthogonal channels. Finally, with the information of an outage indicator, we propose the estimation algorithm for average signal-to-interference-noise ratio (SINR) of wireless links. From numerical results, we confirm that the utility of capacity with outage is maximized and the average performance of proposed algorithm converges to the desired maximizing point.