On-demand quantum memory is an important step towards practical applications in various quantum information tasks such as long-distance entanglement distribution, quantum computation, and quantum networks. In this work, based on stimulated Raman adiabatic passage (STIRAP) protocol, we introduce a controllable delay between the reading pulse and writing pulse so that the quantum state can be stored in the superconducting waveguide and finally retrieved on demand with high fidelity. Through systematic numerical simulations, we find that if the duration of the writing pulse is set to be in a certain range, the readout unit is capable of retrieving the quantum state stored in the waveguide with high fidelity at any moment after a critical time. Moreover, we also investigate the robustness of our protocol, and find that the fidelity is robust against both the average number of thermal photons in the waveguide and the duration of the reading pulse. The numerical results also show that the pulse area in our protocol is only about one third of that in the original STIRAP protocol. Our protocol provides a practical way to combine the advantages of both on-demand quantum memory and the STIRAP protocol.