The aim of this note is to study properties of the generalized centroid of the semi-prime gamma rings. Main results are the following theorems: (1) Let M be a semi-prime $Gamma$-ring and Q a quotient $Gamma$-ring of M. If W is a non-zero submodule of the right (left) M-module Q, then $WGamma$W $ eq 0. Furthermore Q is a semi-prime $Gamma$-ring. (2) Let M be a semi-prime $Gamma$-ring and $C_{{Gamma}$ the generalized centroid of M. Then $C_{Gamma}$ is a regular $Gamma$-ring. (3) Let M be a semi-prime $Gamma$-ring and $C_{gamma}$ the extended centroid of M. If $C_{gamma}$ is a $Gamma$-field, then the $Gamma$-ring M is a prime $Gamma$-ring.