This paper introduces the design of the second order GCF (Generalized Comb Filter) compensator based on L1 optimization. The problem is represented by a set of nonlinear equations solved by the Newton–Raphson algorithm. The proof of the uniqueness of the solution is also provided. One can reduce the complexity of the design approximating the original set of nonlinear equations by the set of linear equations, which depends only on the passband edge frequency ωp. A design example demonstrates the effectiveness of the proposed design.