Fabless semiconductor industry and government agencies have raised serious concerns about tampering with inserting hardware Trojans (HTs) in an integrated circuit supply chain in recent years. In this paper, a low hardware overhead acceleration method of the detection of HTs based on the insertion of 2-to-1 MUXs as test points is proposed. In the proposed method, the fact that one logical gate has a significant impact on the transition probability of the logical gates in its logical fan-out cone is utilized to optimize the number of the inserted MUXs. The nets which have smaller transition probability than the user-specified threshold and minimal logical depth from the primary inputs are selected as the candidate nets. As for each candidate net, only its input net with smallest signal probability is required to be inserted the MUXs-based test points. The procedure repeats until the minimal transition probability of the entire circuit is not smaller than the threshold value. In order to further optimize the number of required insertions and reduce the overhead, the weighted random pattern technique is also applied. Experiment results on ISCAS'89 benchmark circuits show that our proposed method can achieve remarkable improvement of transition probability with on average 9.50% power, 2.37% delay, and 10.26% area penalty.