We consider the stochastic differential equation $X_t=X₀+{\int }_0^t(A_s+B_s{X}_s)ds+{\int }_0^t{C}_{s}d{Y}_s$, where $A_t$, $B_t$, $C_t$ are nonrandom continuous functions of t, X₀ is an initial random variable, $Y=(Y_t,t\ge 0)$ is a Gaussian process and X₀, Y are independent. We give the form of the solution ($X_t$) to (0.1) and then basing on the results of Plucińska [Teor. Veroyatnost. i Primenen. 25 (1980)] we prove that ($X_t$) is a quasi-diffusion proces.