By using a variant of the quantum inverse scattering method, commutation relationsbetween all elements of the quantum monodromy matrix of the bosonic massiveThirring (BMT) model are obtained. Using those relations, the quantum integrabilityof BMT model is established and the S-matrix of two-body scatteringbetween the corresponding quasiparticles has been obtained. It is observed that forsome special values of the coupling constant, there exists an upper bound on thenumber of quasiparticles that can form a quantum-soliton state of the BMT model.We also calculate the binding energy for a N-soliton state of the quantum BMTmodel