A new robust fixed-order RST controller design approach by convex optimization is proposed in this paper. Only frequency-domain data are considered in the approach for linear time-invariant single-input single-output systems. It is shown that performance specifications given as the infinity norm of the weighted sensitivity functions can be represented as convex constraints in the Nyquist diagram. One of the advantage of the proposed method is that it can deal directly with multi-model uncertainty. Moreover, a solution to a real industrial problem is given showing the effectiveness of the method.