Two-particle cluster theory is applied to study the biaxial nematic phase formed by biaxial molecules interacting with a simplified model proposed by Sonnet et al. [Phys. Rev. E 67 (2003) 061701]. For the temperature dependences of the inteal energy per particle and of the order parameters, the two-particle theory yields an improved result compared with mean field theory. Conceing the phase diagram, the two-particle theory gives the numerical result in qualitative agreement with the mean field theory.