Optical pulse signals of two different wavelengths in the infrared regime were generated in atomic Rb vapor by nonlinear optical frequency mixing using optical pulses generated in a Ti:sapphire laser. The effects of Rb number density, pump laser intensity, and the chirp of laser pulses on the competition characteristics of the two signals were investigated. The results show that the two signals are mainly generated from two coupled parametric six-wave mixings processes, and the signals vary with Rb number density, pump laser intensity and the chirp of pump laser pulses. The competition between the two signals is dominantly governed by phase matching conditions which are closely related to Rb number density, but scarcely related to pump laser intensity and the chirp of pump laser pulses.