In this work we investigate the interaction between spin-zero and spin-one monopoles by making use of an effective field theory based on two-body and four-body interaction parts. In particular, we analyze the formation of bound state of monopole-antimonopole (i.e. monopolium). The magnetic-charge conjugation symmetry is studied in analogy to the usual charge conjugation to define a particle basis, for which we find bound-state solutions with relatively small binding energies and which allows us to identify the bounds on the parameters in the effective Lagrangians. Estimations of their masses, binding energies and scattering lengths are performed as functions of monopole masses and interaction strength in a specific renormalization scheme. We also examine the general validity of the approach and the feasibility of detecting the monopolium.
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