Since the efficiency of rule mining and validity of recommendation are not high in personalized friends recommendation based on association rules, an improved association rule algorithm based on bitmap and hashing, namely BHA, was proposed. The mining time of frequent 2-itemsets was decreased by introducing hashing technique in this algorithm, and the irrelevant candidates were compressed to decrease the traversal of data by using bitmap and relevant properties. In addition, on the basis of BHA, a friend recommendation algorithm named STA was proposed based on similarity and trust. The problem of no displayed trust relationship in microblog was resolved effectively through trust defined by similarity of out-degree and in-degree; meanwhile, the defect of the similarity recommendation without considering users' hierarchy distance was remedied. Experiments were conducted on the user data of Sina microblog. In the comparison experiment of digging efficiency, the average minging time of BHA was only 47% of the modified AprioriTid; in the comparison experiment of availability in friend recommendation with SNFRBOAR (Social Network Friends Recommendation algorithm Based On Association Rules), the precision and recall of BHA were increased by 15.2% and 9.8% respectively. The theoretical analysis and simulation results show that STA can effectively decrease average time of mining rules, and improve the validity of friend recommendation.