We use the Magnus expansion method to study the problem of coherent population transfer from the ground state to the indirect exciton state in a three-level asymmetric double quantum-dot system driven by a single laser pulse. By the first-order Magnus expansion of the time-evolution unitary operator of the quantum system, we analytically obtain the pulse-area conditions for achieving complete population transfer of the asymmetric double quantum-dot system without rotation wave approximation. Then, we solve the time-dependent Schrödinger equation of the system for numerical verification of the pulse-area conditions. Furthermore, we compare the performance of the Gaussian pulse, the multi-period cosine pulse, and the single-period cosine pulse in population transfer. The results show that all three pulses can achieve complete population transfers as long as the pulse-area conditions are satisfied, which reveals the physical significance of optical field amplitude in population transfer. The robustness analysis of the three pulse schemes indicates that the single-period cosine pulse is superior to the other two in the resistance against unstable laser pulse parameters and the decoherence effect. This work offers a vital reference for precise optical field control over the quantum state of asymmetric quantum-dot systems, which is of significant value in quantum optics and quantum information science fields.