The universal filtered multi-carrier (UFMC) has been taken as a promising candidate for future wireless communication, where a finite impulse response filter is employed to shape the waveform and enhance its resistance to inter-carrier interference. In previous studies, the Dolph-Chebyshev filter had been used due to its low-sidelobe levels, but at the cost of low flexibility to filter the performance control. Hence, this paper puts forward an effective scheme to design an anti-interference filter for UFMC system, where the Nyquist condition (or sampling inter-symbol interference equivalently), the in-band distortion, and the out-of-band emission are taken into consideration. First, this paper models the filter design as a constrained minimax optimization concerning above-mentioned filter performance indexes. Then, the original nonconvex constraints on Nyquist condition are approximately transformed to a linear matrix inequation and two linear inequations. Finally, the optimization problem is solved by semidefinite programming. The numerical examples explicitly demonstrate the flexible performance tradeoff of the proposed method, in which the included filter performance indexes can be effectively controlled. Moreover, the bit-error-rate (BER) tests of the UFMC system confirms the effectiveness of our study, where the designed filters show BER advantages over filters of the previous literature. Therefore, the proposed waveform shaping filters can benefit variant applications of UFMC for its flexible performance tradeoffs as well as the improved anti-interference performance.