We have constructed a Geometric quadratic stochastic operator generated by 2-partition ξ of singleton defined on countable state space X , where X =0,1,2,.... We have studied the trajectory behavior of such operator for any initial measure µ ε S(X, F) . It is shown that such operator converges to a fixed point which indicates the existence of the strong limit of the sequence Vn(µ) . This follows that such operator is a regular transformation. © 2019 Penerbit UTM Press. All rights reserved.