CsFeBr3 is an S = 1 hexagonal antiferromagnet that has a singlet ground state owing to its large easy-plane single-ion anisotropy. The critical behavior of the magnetic-field-induced phase transition for a magnetic field parallel to the c axis, which can be described by the Bose -Einstein condensation (BEC) of magnons under the U (1) symmetry, was investigated via magnetization and specific heat measurements down to 0.1 K. For the specific heat measurement, we have developed a method of effectively suppressing the torque acting on a sample with strong anisotropy that uses the spin dimer compound Ba2CoSi2O6Cl2 with large and anisotropic Van Vleck paramagnetism. The temperature dependence of the transition field Hc(T ) was found to follow the power-law Hc(T ) − Hc ∝ T φ with a critical exponent of φ = 1.50 ± 0.02 and critical field of Hc = 2.60 T. This result verifies the universality of the three-dimensional BEC of magnons described by φBEC = 3/2.