The present paper describes an application of non-parametric shape optimization to disc brake squeal phenomena. A main problem is defined as complex eigenvalue problem in which the real part of the complex eigenvalue causing the brake squeal is chosen as an objective cost function. The Fre´chet derivative of the objective cost function with respect to the domain variation, named as the shape derivative of the objective cost function, is evaluated using the solution of the main problem and the adjoint problem. A selection criterion of the adoptive mode number in component mode synthesis (CMS), which is used in the main problem, is presented in order to reduce the computational error in complex eigenvalue pairs. A scheme to solve the shape optimization problem is presented using an iterative algorithm based on the H1 gradient method for reshaping. For an application of the optimization method, a numerical example of a practical disc brake model is presented. The numerical result illustrates that the real part of the target complex eigenvalue monotonously decreases until it reach zero.