In this paper, the problem of joint transmit power and bandwidth allocation over multiple channels is investigated for a secondary user in underlay mode, when partial information of interference channel is known. The target is to maximize the capacity of a secondary user under a probabilistic constraint of the interference to the primary user. A robust optimization problem is formulated, which is nondeterministic and cannot be solved directly. We then transform the original optimization problem into an equivalent convex optimization problem. For general case, an optimal solving algorithm, which is a combination of analytical and bisection-search methods, is given. For some special cases, simple and optimal solving algorithms are also devised. Numerical results are presented to show that our proposed optimal algorithm has low computation complexity when the number of channels is not large and can achieve global optimal utility in general case and our proposed simple algorithms have much lower computation complexity and can achieve global optimal utility in special cases.