The advanced study of Cr3+ impurity ions in the Van Vleck paramagnet TmAl3(BO3)(4) is reported in this work. The angular dependence of the electron paramagnetic resonance spectrum from Cr3+ ion has been studied in detail, and the parameters of spin Hamiltonian were evaluated at T = 11 K [g = 1.980 +/- 0.002; D = (-0.534 +/- 0.001) cm(-1); E = (0.027 +/- 0.005) cm(-1)]. It was shown that the Cr3+ ions substitute trivalent aluminum ions and form a system of three magnetic equivalent ions rotated through 120 degrees relative to each other. The deviation of the Zaxis from the C-3-axis for Cr3+ ions was found to be 2.5 degrees. A significant temperature dependence of g and D parameters has been found. It was shown that a strong broadening of the EPR lines depends on the dipole and exchange fields generated by the magnetic moment of the thulium ion. The contributions of the excited states of the Tm3+ ion to the temperature-dependent component of the Cr3+ EPR line-width have been discussed.