Many combinatorial problems, including a variety of combinatorial optimization problems, can be naturally formulated as a constraint satisfaction problem (CSP). We develop in this paper a tabu search-based algorithm for the CSP as a foundation for a general problem solver. In addition to the basic components of tabu search, we develop a number of elaborations, such as an automatic control mechanism for the tabu tenure, modification of the penalty function to handle objective functions, and enlargement of the neighborhood by allowing swap operations. Computational results with our algorithm are reported for various problems selected from a wide range of applications, i.e., graph coloring, generalized assignment, set covering, timetabling and nurse scheduling. Our results appear to be competitive with those of existing algorithms specially developed for the respective problem domains.