Due to the simplicity and flexibility of the structure of the Second-Order Generalized Integrator based Quadrature Signal Generator (SOGI-QSG), it has been widely used over the past decade for many applications such as frequency estimation, grid synchronization, and harmonic extraction. However, the SOGI-QSG will produce errors when its input signal contains a dc component or harmonic components with unknown frequencies. The accuracy of the signal detection methods using it may hence be compromised. To overcome the drawback, the First-Order System (FOS) concept is first used to illustrate the principle of the SOGI-QSG, based on which, an improved Second-Order SOGI-QSG (SO-SOGI-QSG) is then proposed by referring the relationship of the standard FOS and the second-order system. The proposed SO-SOGI-QSG inherits the simplicity of the SOGI-QSG, while it has much stronger attenuation ability for both low- and high-frequency components. A detailed parameter design procedure for the SO-SOGI-QSG is provided in this paper as well. The effectiveness of the proposed SO-SOGI-QSG is finally validated by experimental results.