Abstract W$\, 51\,$A is one of the most active star-forming regions in the Milky Way, and includes copious amounts of molecular gas with a total mass of ${∼ }6\times 10^{5}\, M_{⊙ }$. The molecular gas has multiple velocity components over ∼20 km s−1, and interactions between these components have been discussed as the mechanism that triggered the massive star formation in W$\, 51\,$A. In this paper, we report on an observational study of the molecular gas in W$\, 51\,$A using the new 12CO, 13CO, and C18O (J = 1–0) data covering a 1${^{∘}_{.}}$4 × 1${^{∘}_{.}}$0 area of W$\, 51\,$A obtained with the Nobeyama 45 m telescope at 20′ resolution. Our CO data resolved four discrete velocity clouds with sizes and masses of ∼30 pc and 1.0–$1.9\times 10^{5}\, M_{⊙ }$ around radial velocities of 50, 56, 60, and 68 km s−1. Toward the central part of the Hii region complex G49.5−0.4 in W$\, 51\,$A, in which the bright stellar clusters IRS 1 and IRS 2 are located, we identified four C18O clumps having sizes of ∼1 pc and column densities of higher than 1023 cm−2, which are each embedded within the four velocity clouds. These four clumps are concentrated within a small area of 5 pc, but show a complementary distribution on the sky. In the position–velocity diagram, these clumps are connected with each other by bridge features having weak intensities. The high intensity ratios of 13CO (J = 3–2)$/$(J = 1–0) also indicate that these four clouds are associated with the Hii regions, including IRS 1 and IRS 2. We also reveal that, in the other bright Hii region complex G49.4−0.3, the 50, 60, and 68 km s−1 clouds show a complementary distribution, with two bridge features connecting between the 50 and 60 km s−1 clouds and the 60 and 68 km s−1 clouds. An isolated compact Hii region G49.57−0.27 located ∼15 pc north of G49.5−0.4 also shows a complementary distribution and a bridge feature. The complementary distribution on the sky and the broad bridge feature in the position–velocity diagram suggest collisional interactions among the four velocity clouds in W$\, 51\,$A. The timescales of the collisions can be estimated to be several 0.1 Myr as crossing times of the collisions, which are consistent with the ages of the Hii regions measured from the sizes of the Hii regions with the 21 cm continuum data. We discuss a scenario of cloud–cloud collisions and massive star formation in W$\, 51\,$A by comparing these with recent observational and theoretical studies of cloud–cloud collision.