Starting from equation of motion and continuity equation for electrons along with Maxwell's equations, the dispersion relation is obtained for a waveguide filled with warm, anisotropic plasma under the influence of infinite magnetic field in a direction perpendicular to the direction of propagation. The plasma is assumed to be weakly ionized, in which electrons are warm with an average temperature higher than the temperature of neutral particles, and in which electrons undergo ordinary hardsphere elastic type collisions with the neutral molecules. For simplicity, collisions with electrons are taken care of by a constant collisions frequency independent of velocity. The plasma model may be considered as being a single fluid medium in which only the electron component participates in the phenomena of interest. From the wave equations for longitudinal component of electric and magnetic fields, it is concluded that TE modes are unaffected by the presence of collisional plasma. However, the characteristic equation for TM modes get modified by some additional terms which are wholly dependent on collision frequency.