Let $X$ be a linear space over a field $\mathcal K$ of scalars and let $R_1(X)$ be the set of all generalized right invertible operators in $L(X)$. Consider the general linear equation with generalized right invertible operator $V$ of the form $$\sum\limits_{m=0}^M\sum\limits_{n=0}^NV^mA_{mn}V^nx=y, \quad y\in X,$$ where $A_{mn}\in L_0(X)$, $A_{MN} = I$, $A_{mn}X_{M+N−n}\subset X_m$, $X_j := \mathrm{dom}V^j$. Similar equations with right invertible operators were studied by Przeworska-Rolewicz, and others (see [1], [2], [3]). In [4], N. V. Mau and N. M. Tuan constructed the generalized right invertible operators. In this paper, we present some new properties of generalized right invertible operators and then apply them to obtain all solutions of the general linear equations for the genezalized right invertible operator $V$ with non-commutative cofficients.