It is still an open problem whether or not for l an integer greater than 1 and  the Hausdorff dimension of the graph of the Weierstrass function  equals to  This paper provides a partial solution of the open problem, i.e., it is shown that the Hausdorff dimension of the graph of Weierstrass function equals to  for large integers l. Moreover, our proof is based on the method, it is called power law combining  technique. This method may be used to treated some non-linear problem.

Hausdorff dimension, Weierstrass function, approximately self-similarity, merger rule.