The three-dimensional incompressible Boussinesq system is one of the important equations in fluid dynamics. The system describes the motion of temperature-dependent incompressible flows. And the temperature naturally has diffusion. Very recently, Elgindi, Ghoul and Masmoudi constructed a $C^{1,\alpha}$ finite time blow up solutions for Euler systems with finite energy. Inspired by their works, we constructed $C^{1,\alpha}$ finite time blow-up solution for Boussinesq equations where temperature has diffusion and finite energy. The main difficulty is that the Laplace operator of temperature equation is not coercive under Sobolev weighted norm which is introduced by Elgindi. We introduced a new time scaling formulation and new weighted Sobolev norms, under which we obtain the coercivity estimate. The new norm is well-coupled with the original norm, which enable us to finish the proof. This is a jointed work with Gao Chen and Zhang Xianliang.