Summary: In this paper, we define \(g\)-convergence and \(g\)-Cauchy of double sequences in \(g\) metric spaces. Also we prove that \(g\)-limit is unique and every \(g\)-convergent double sequence is a \(g\)-Cauchy sequence. Additionally \(g\)-statistical convergence of double sequences is introduced and the theorem giving the relationship between statistical convergence and strongly Cesàro summability in a \(g\)-metric space is demonstrated. Further, we put forward the notations of \(g\) lacunary statistical convergence and \(g\)-strongly lacunary convergence of double sequences and we also present some inclusion theorems.