Orthogonal Frequency Division Multiplexing (OFDM) systems have been widely used as a communication system. In OFDM systems, there are two main problems. One of them is that OFDM signals have high Peak-to-Average Power Ratio (PAPR). The other problem is that OFDM signals have large side-lobes. In particular, to reduce side-lobes, Universal-Filtered OFDM (UF-OFDM) systems have been proposed. In this paper, we show criteria for designing filters for UF-OFDM systems and a method to obtain the filter as a solution of an optimization problem. Further, we evaluate PAPR with UF-OFDM systems. Our filters have smaller side-lobes and lower Bit Error Rate than the Dolph-Chebyshev filter. However, the PAPR for signals with our filters and the Dolph-Chebyshev filter are higher PAPR than those with conventional OFDM signals.