We investigate the phase separation of Lennard-Jones (LJ) particles in the presence of cosolute crowders using molecular dynamics simulations. In the absence of crowders, LJ particles phase-separate and form liquid and vapor phases only when the attraction between LJ particles is strong enough such that k(B)T/epsilon is less than 1.085, where e is the attraction strength of the LJ potential, k(B) is the Boltzmann constant, and T is the temperature. On the other hand, the phase separation of LJ particles is observed even for larger k(B)T/epsilon and thus for weaker attractions when volume exclusive, repulsive crowders are present. Although the impact of crowding becomes less significant as the attraction between crowders and LJ particles is increased, the phase separation observed from simulations containing both nonattractive and attractive crowders shows that the crowding-induced phase separation by nonattractive crowders is still very significant even in the presence of other attractive crowders. This occurs because not only LJ particles but also attractive crowders are subject to the excluded volume effect of nonattractive crowders and found together in the condensed phase. This study suggests that the excluded volume effect in the crowded nuclear environment may play a crucial role in the formation and maintenance of biological structures in a cell, such as nuclear bodies including nucleoli and cajal bodies.