The American put valuation problem is very important and complicated in the Option Pricing Theory (OPT), and so far the appropriate continuous-time pricing model and compact valuation formula for the American put option have not been found. On the basis of the research works of many scholars such as Black, scholes, Parkinson, Brennan, Schwartz, Rendleman, Bartter, Cox, Ross and Rubinstein etc., making use of the notion of limitation and the binomial approach, this paper constructs and realizes gradually approaching algorithm of pricing American put options. Its reasonability, convergence and validity are tested by computer programming. The results show that this algorithm can effectively resolve the American put valuation problem.