Since Watson and Crick proposed the DNA structure in 1953, the Watson-Crick model of the DNA double helix has provided enormous impetus for research in the emerging fields of molecular genetics and biochemistry. The confluence of scientific research activities from molecular biology, computer science, mathematics, physics, and other technologies leads to recent establishment of bioinformatics. Bioinformatics studies the important information flow and discovers new knowledge from the fundamental elements in biological systems by using biological framework, mathematical theories, computational algorithms, and tools from mathematics and computer science. Advances in bioscience research and biotechnology experiments have produced enormous volume of scientific data. However, the rate of data generation is far outpacing scientists' ability to analyze the data and to understand them fully. Bioinformatics provides great opportunities for developing novel data mining methods in order to discover knowledge from this set of scientific data. One of the major objectives of this paper is to conduct a survey of some well-established existing data mining methods that perform potential bioinformatics data mining tasks and to raise several issues in data mining for bioinformatics in the future.