Statistical theory of nematic liquid crystal whose constituent molecules are biaxial ellipsoids is proposed. The method is suggested which enables one to calculate exactly the second virial coefficient for the system of biaxial ellipsoidal particles and to obtain a simple approximation formula for the third one. By means of the so-called gamma-expansion, the thermodynamic potential of the system is constructed and equations of the thermodynamic and orientational state are obtained. The influence of the anisometric degree (i.e. the measure of biaxiality) of the particles on the features of orientational behavior and phase transitions among the isotropic, uniaxial and biaxial nematic phases is studied. A phase diagram for a system of biaxial ellipsoids has been calculated. It is shown that the so-called self-dual point takes place with high degree of accuracy. In the limiting cases (molecules are spheres or ellipsoids of revolution) our results are identical with earlier known ones.