The idea of the statistical convergence of single sequences was first studied by

*H. Fast* [Colloq. Math. 2, 241–244 (1951;

Zbl 0044.33605)]. The idea of the statistical convergence of double sequences was first introduced by

*E. Mursaleen* and

*H. H. Osama* [J. Math. Anal. Appl. 288, No.1, 223–231 (2003;

Zbl 1032.40001)]. Most of the existing works on statistical convergence have been restricted to real or complex sequences. The authors give an extension of statistical convergence of double sequences to topological groups and give some theorems in this general setting.