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Aiming at the system instability caused by the uncertainty of the extreme learning machine( ELM) hidden nodes and the problem of overburdening large data calculations, this paper proposed an optimization algorithm based on the adaptive and momentum method (AdaMom) . This algorithm constructed a continuously differentiable objective function, and calculated the adaptive learning rate during the gradient descent process,obtained the exponentially weighted average of the product of the adaptive learning rate and the gradient. At last it obtained the hidden layer output weight matrix corresponding to the minimum value of the loss function through iteration. The experimental results show that in the training of the same benchmark data set, the AdaMom- ELM algorithm has very good generalization performance and robustness, which improves the computational efficiency. [ABSTRACT FROM AUTHOR]