We propose the generation of a high-speed four-level pulse amplitude modulated (PAM4) signal by combining two on-off keying (OOK) signals obtained by overdriving two Mach-Zehnder modulators (MZMs). By using this method, we can overcome the limited modulation bandwidth of the MZM and generate the high-speed PAM4 signal (faster than the PAM4 signal generated by modulating an MZM with a four-level electrical signal). For a demonstration, we generate the 95-Gb/s PAM4 signal by combining two OOK signals obtained from the bandwidth-limited MZM having a 3-dB bandwidth of only 10.5 GHz. In comparison, when we generate the PAM4 signal by using the conventional method, it is not possible to increase the bit rate to be faster than 60 Gb/s. We also successfully demonstrate the transmission of the 95-Gb/s PAM4 signal generated by the proposed method over 4 km of the standard single-mode fiber. (c) 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement