In order to avoid the problem caused by the operator order, an adaptive algorithm named the adaptive derivative-assembled pseudo-Trotter Ansätze variational quantum eigensolver(ADAPT-VQE) has been proposed. The most prominent feature of ADAPT-VQE is constructing the Ansätze with unfixed number of operators and assembling the operators adaptively. In each iteration, the algorithm identifies the operator with the largest gradient and adds this single operator to the left end of the Ansätze, with a new variational parameter. The operation is repeated until reaching the convergence of the energy. ADAPT-VQE is robust to the strongly correlated molecule and generates an Ansätze with much less number of parameters than the UCCSD Ansätze. The adaptive feature of ADAPT-VQE ensures to achieve exact results at convergence and finally generates compact Ansätze with a proper operator order.