2 (NG) bosons associated with the spontaneous breaking of the chiral symmetry and their interactions are determined uniquely by the low-energy theorem. This allows us to construct low-energy effective theories including the baryons as light degrees of freedom naturally, and to investigate properties of hadrons even at finite baryon density using them. Furthermore, because there are many studies of the lattice QCD simulations, we can make a comparison of results from effective theories with those from the lattice analyses [5–7]. Actually, in two-color QCD, the phase structure at finite baryon number density µ$_{B}$ was studied [3] using the chiral Lagrangian including the pseudo-NG bosons, having masses of M$_{π}$ , which are associated with the chiral symmetry breaking of SU (2 N$_{f}$ ) → Sp (2 N$_{f}$ ). It was shown that the phase transition from the symmetric phase of the baryon number U (1)$_{B}$ to the broken phase takes place at µ$_{B}$ = M$_{π}$ , triggered by the condensation of the baryonic pseudo-NG bosons. There, the density dependences of the masses of pseudo-NG bosons are also studied and it was found that a baryonic boson becomes the massless NG boson in the U (1)$_{B}$ broken phase. The density dependences of “vector” bosons (In this paper we call “vector” bosons which consist of mesons with J P = 1 − and diquark baryons with J P = 1 $^{+}$.) are studied in the lattice simulation [6, 7]. It was shown that the mass of “ ρ ” meson decreases with µ$_{B}$ [6, 7], and that the mass of anti-baryon with J P = 1 + increases linearly with µ$_{B}$ for µ$_{B}$ ≲ M$_{π}$ while that of baryon decreases linearly [7]. For µ$_{B}$ ≳ M$_{π}$ , the baryon mass is not yet clearly confirmed. On the other hand, the behaviors of the masses were also studied in an effective model [8]. It is interesting to study the masses in a general effective model which can include several models with the parameters chosen suitably. In this paper we construct a low energy effective Lagrangian for the two-color QCD including the “vector” bosons (mesons with J P = 1 − and diquark baryons with J P = 1 $^{+}$) in addition to the pseudo-NG bosons (mesons with J P = 0 − and baryons with J P = 0 $^{+}$). The effective Lagrangian is composed based on the chiral symmetry breaking pattern of SU (2 N$_{f}$ ) → Sp (2 N$_{f}$ ) in the framework of the hidden local symmetry (HLS) [9–11], and the “vector” bosons are introduced as the gauge bosons of the Sp (2 N$_{f}$ ) HLS. The HLS is equivalent to other models for “vector” bosons such as the CCWZ matter field [12], the tensor field [13] and the Massive Yang-Mills field [14]. Furthermore, it is possible to perform the systematic derivative expansion in the HLS [11, 15–17] , which allows us to study the parameter dependences of the masses at finite density in a systematic way.