Molecular quantum magnetism involving an isolated spin state is of particular interest due to the characteristic quantum phenomena underlying spin qubits or molecular spintronics for quantum information devices, as demonstrated in magnetic metal-organic molecular systems, the so-called molecular magnets. Here we report the molecular quantum magnetism realized in an inorganic solid Ba3Yb2Zn5O11 with spin-orbit coupled pseudospin-½ Yb(3+) ions. The magnetization represents the magnetic quantum values of an isolated Yb4 tetrahedron with a total (pseudo)spin 0, 1 and 2. Inelastic neutron scattering results reveal that a large Dzyaloshinsky-Moriya interaction originating from strong spin-orbit coupling of Yb 4f is a key ingredient to explain magnetic excitations of the molecular magnet states. The Dzyaloshinsky-Moriya interaction allows a non-adiabatic quantum transition between avoided crossing energy levels, and also results in unexpected magnetic behaviours in conventional molecular magnets.