Abstract: Let Ω be a multiplicative left(right) cancellative monoid, S=_x∈ΩS_x and T=_x∈ΩT_x be two Ω-graded rings with 1, and B=_SB_T=_{x∈ΩBx be a Ω-graded (S,T)-bimodule, R is the graded triangular matrix ring determined by S,T and SBT. It is shown that if SB is graded faithful then R is a graded nonsingular ring if and only if T is a graded nonsingular ring and BT is a graded nonsin gular module.}

Key words: graded triangular matrix ring, graded essential submodule, graded nonsingular ring, graded nonsingular module