A time-of-flight (TOF) detector has been used in the BESIII experiment to provide charged particle identification. In this paper, we present a novel high performance differential amplifier, which has been designed for amplifying the signals from the detectors. The preamplifier can amplify differential signals, which can help to eliminate the common mode pickup, and increase the signal-to-noise ratio (SNR). Bilinear gain is one of the features of this preamplifier, which greatly increases the dynamic range and avoids the dead time of the preamplifier. In order to describe the bilinear gain, a 4-parameter function is developed. And this 4-parameter function can also be used in the calibration of the time walk caused by the amplitude due to the bilinear gain. The preamplifier has a gain about 10V/V with a small signal and about 1.0V/V with a large signal. The rise time of the preamp is less than 2 ns. A time-of-flight (TOF) detector has been used in the BESIII experiment to provide charged particle identification. In this paper, we present a novel high performance differential amplifier, which has been designed for amplifying the signals from the detectors. The preamplifier can amplify differential signals, which can help to eliminate the common mode pickup, and increase the signal-to-noise ratio (SNR). Bilinear gain is one of the features of this preamplifier, which greatly increases the dynamic range and avoids the dead time of the preamplifier. And this 4-parameter function is developed. And this 4-parameter function is also used in the calibration of the time walk caused by the amplitude due to the bilinear gain. The preamplifier has a gain about 10V / V with a small signal and about 1.0V / V with a large signal. The rise time of the preamp is less than 2 ns.