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A novel neural network arithmetic was employed in sparseness points cloud data surface interpolation and reconstruction. Radial basis function neural network and simulated annealing arithmetic was combined. The new arithmetic can approach any nonlinear function by arbitrary precision, and also keep the network from getting into local minimum. Global optimization feature of simulated annealing was employed to adjust the network weights. MATLAB program was compiled, experiments on sparseness points cloud data have been done employing this arithmetic, the result shows that this arithmetic can efficiently approach the surface with 10-4 mm error precision, and also the learning speed is quick and reconstruction surface is smooth. Different methods have been employed to do surface reconstruction in comparison, the sum squared error is 6.7times10-8 mm employing the algorithmic proposed in the paper, the one is 1.34times10-6 mm with same parameters employing radial basis function neural network. Backpropagation learning algorithm network does not converge until 3500 iterative procedure.