The positron impact-ionization of atomic hydrogen in the presence of a linearly polarized bichromatic field is investigated in the second Bo approximation. The field is composed of a fundamental frequency and its second harmonic. The state of positron in the field is described by the Volkov wavefunction, and the continuum state of the ejected electron is described by the Coulomb-Volkov wavefunction. The dressed ground state of target is a first order time-dependent perturbative wavefunction. The triple differential cross sections and their dependencies on laser field parameters are discussed. Numerical results demonstrate that the second-order effect plays a crucial role in understanding the laser-assisted positron scattering process.