Accurate free-form deformation is designed to solve sampling problem and can generate high quality deformation result. But it is difficult to achieve real-time performance due to high computational costs. The authors ever proposed a GPU acceleration algorithm to solve this problem. In this paper, a new GPU algorithm is proposed to further accelerate accurate free-form deformation significantly, where the deformed object is represented in terms of triangular Bezier surfaces. The intensive computations involved in the accurate free-form deformation are designed on GPU via CUDA totally. After careful derivations, the computations of generating the triangular Bezier surfaces and their tessellations are abstracted into two matrix multiplications. Since the relevant matrices can be reused for all triangular Bezier surfaces, the computations can be greatly accelerated via CUBLAS, i.e. an API of linear algebra sub-programs on GPU. Finally, the tessellated surfaces are output to a vertex buffer object and rendered via OpenGL efficiently. Experimental results show that the proposed algorithm is more efficient than the previous GPU acceleration algorithm and tessellation shader algorithm.