To overcome the challenge of taking a balance among the circuit depth, accuracy as well as time cost and simultaneously maintaining the automaticity of the algorithm, in this work, we introduce a new strategy named the amplitude reordering (AR), which can generate an quasi-optimal order for a collection of arbitrarily given operators without introducing additional operators. The essence of the AR method is to sort the operators iteratively according to their corresponding amplitudes, so that the scalar part of X can be minimized and the operator tensor product by the sorted order is close to the non-Trotterized Ansätze which is order-independent. With the assistance of this operator order optimization method, it is permitted to append several operators with an apposite order in each adaptive iteration, subsequently the number of adaptive iterations and thus N T are reduced. As a result, under the premise of generally no increase in the circuit depth and no loss of the accuracy, a speedup of several times to even more than ten times is achieved by using the AR-equipped AAs (AR-AAs), as will be demonstrated by the subsequent numerical simulations. This paper is organized as follows. After a brief introduction of two AAs, ADAPT-VQE and AES-VQE, in Section 2.1, our proposed AR method is detailed in Section 2.2. Then, a general workflow of AR-AAs is given in Section 2.3, where the AR-ADAPT-VQE and AR-AES-VQE algorithms are demonstrated in more detail. The numerical benchmark tests of (AR-)ADAPT-VQE and (AR-)AES-VQE are shown in Section 3. Finally a concluding remark is given in Section 4.