Magnetic properties were investigated in La3Re2O10 with Re-2 clusters. An Re-2 cluster has three 5d electrons in nondegenerated cluster orbitals, resulting in the construction of S = 1/2 spin per Re-2 cluster. La3Re2O10 has a Weiss temperature of approximately -110 K and exhibits a broad maximum in the temperature dependence of magnetic susceptibility, suggesting the development of short-range ordering among cluster spins at low temperatures. La3Re2O10 shows an antiferromangetic ordering at T-N = 18.7 K, and below T-N, La3Re2O10 shows a strong field dependence of magnetization, which indicates several phase transitions. The magnetic properties of La3Re2O10 are summarized as a magnetic field-temperature phase diagram, which suggests an unconventional multicritical point. Such a phenomenon cannot be interpreted only by the magnetic interactions owing to phase rule, suggesting the existence of other degrees of freedom for making an exotic phase transition.