Random testing has been used for years in both software and hardware testing. It is well known that in random testing each test requires to be selected randomly regardless of the test previously generated. However, random testing could be inefficient for its random selection of test patterns. This paper, based on the random testing, introduces the concepts of Maximum Distance Testing (MDT) for VLSI circuits in which the total distance among all test patterns is chosen maximal so that the set of faults detected by one test pattern is as different as possible from that of faults detected by the tests previously applied. Procedure of constructing a maximum distance testing sequence (MDTS) is described in detail. Experimental results on Benchmark as well as other circuits are given to evaluate the performances of our new approach.