It has commonly been acknowledged that solving constrained problems with a variety of complex constraints is a challenging task for genetic algorithms (GA). Existing methods to handle constraints in GA are often computationally expensive, problem dependent or constraint specific. In this paper we introduce an idea of constraint consistent GA (CCGA) as an attempt to overcome those drawbacks. Constraint handling is based on general constraint consistency methods that prune the search space and thus reduce the search effort in CCGA. Unfeasible solutions are detected and eliminated from the search space at each stage of CCGA simulation process to support genetic operations in producing feasible solutions. A number of well known standard genetic operators are adapted to take advantage of provided constraint consistency during initialization, crossover and mutation. Initial experiments indicate that in the terms of the solution quality and the number of iterations the constraint consistency based approach in CCGA can outperform other constraint handling methods in GA for a number of selected test problems.