Efficiently controlling the trapping process is very significant in the study of trapping problem in diverse dynamic processes. In this paper, we explore the trapping efficiency on a family of scale-free tree networks with a deep trap positioned at an initial node, which is controlled by three different strategies. In the first technique, the transition probability is modified by an edge weight parameter. In the second method, the transition probability is controlled by a delay parameter. In the third approach, we use the delay parameter and weight parameter simultaneously to control the trapping process. For all the three control methods, the analytical results of average trapping time (ATT) exactly agree with the numerical results. The result of the first control strategy shows that the average trapping time can scale sublinearly, linearly or superlinearly by modifying the weight parameter. The analytic expression of the ATT in the second method shows that the delay parameter can only modify the main coefficient of ATT, but cannot change the dominant behavior of trapping efficiency. The explicit expression of average trapping time when random walk on scale-free tree network is controlled by the third method shows that it is a fine control. We can get desired trapping efficiency by changing the weight parameter and the delay parameter simultaneously. This work provides a better understanding of controlling the trapping process in a family of scale-free tree networks.