By an explicit calculation we demonstrate that the triple gauge-ghost vertices in a general renormalizable {{mathcal {N}}}=1 supersymmetric gauge theory are UV finite in the two-loop approximation. For this purpose we calculate the two-loop divergent contribution to the bar{c}^+ V c-vertex proportional to (C_2)^2 and use the finiteness of the two-loop contribution proportional to C_2 T(R) which has been checked earlier. The theory under consideration is regularized by higher covariant derivatives and quantized in a manifestly {{mathcal {N}}}=1 supersymmetric way with the help of {{mathcal {N}}}=1 superspace. The two-loop finiteness of the vertices with one external line of the quantum gauge superfield and two external lines of the Faddeev–Popov ghosts has been verified for a general xi -gauge. This result agrees with the nonrenormalization theorem proved earlier in all orders, which is an important step for the all-loop derivation of the exact NSVZ beta -function.