Let (M, ω) be a compact connected Kähler manifold of complex dimension four and let [χ] ∈ H 1,1 (M ; R). We confirmed the conjecture by Collins-Jacob-Yau [8] of the solvability of the deformed Hermitian-Yang-Mills equation, which is given by the following nonlinear elliptic equation i arctan(λ i ) = θ, where λ i are the eigenvalues of χ with respect to ω and θ is a topological constant. This conjecture was stated in [8], wherein they proved that the existence of a supercritical C-subsolution or the existence of a C-suboslution when θ ∈ ((n−2)+2/n)π/2, nπ/2 will give the solvability of the deformed Hermitian-Yang-Mills equation. Collins-Jacob-Yau conjectured that their existence theorem can be improved when θ ∈ (n − 2)π/2, ((n − 2) + 2/n)π/2 , where n is the complex dimension of the manifold. In this paper, we confirmed their conjecture that when the complex dimension equals four and θ is close to the supercritical phase π from the right, then the existence of a C-subsolution implies the solvability of the deformed Hermitian-Yang-Mills equation.