By using the split-step fast Fourier transform (SSFFT) method, we numerically study the collision properties between two bright solitons in the growth Bose–Einstein condensates (BECs) with different interaction strengths under a harmonic potential. It is shown that the soliton’s collision property of the condensates can be controlled by adjusting the gain term, the initial position and the interaction strength between atoms. The number of collisions of the two bright solitons decreases first, then increases, with increasing the values of the gain term. As the initial distance between solitons increases, the number of collisions between the two bright solitons is reduced, and the first collision time is also postponed. The increase in interaction strength between atoms delays the collision time of the two bright solitons. Meanwhile, a critical interaction strength between atoms is found, the amplitude of the soliton’s first collision peak increases slowly when the interaction strength is less than the critical value, but the amplitude increases sharply when the interaction strength is more than the critical value.