Vector coherent state theory (VCS), developed for computing Lie group and Lie algebra representations and coupling coefficients, has been used for many groups of interest in actual physical applications. We show that VCS construction of a rotor type can be performed for the SO(5) ~ Sp(4) quasi-spin group where the relevant physical subgroup SU(2) x U(1) is generated by the isospin operators and the number of particle operators.