© 2014, Na Nan and Charoensawan; licensee Springer. In this work, we give the notions of coupled g-coincidence point and [InlineEquation not available: see fulltext.]-increasing property of F for mappings [InlineEquation not available: see fulltext.] and [InlineEquation not available: see fulltext.] and prove the existence and uniqueness of a coupled g-coincidence point theorem for mappings [InlineEquation not available: see fulltext.] and [InlineEquation not available: see fulltext.] with φ-contraction mappings in complete metric spaces without the [InlineEquation not available: see fulltext.]-increasing property of F and the mixed monotone property of G. Further, we apply our results to the existence and uniqueness of a coupled g-coincidence point of the given mappings with the [InlineEquation not available: see fulltext.]-increasing property of F and the mixed monotone property of H in partially ordered metric spaces.