A novel output-only subspace identification method is proposed to estimate the structural parameters of a shear-beam building under unknown ground excitation. The unique feature of the method is that both the structural parameters and the ground acceleration can be identified using only the absolute acceleration response, and no displacement and velocity responses are required. The method uses two subspace identification techniques sequentially and iteratively. The first technique extracts modal parameters of the building (natural frequencies, damping ratios, and mode shapes) using the absolute acceleration response and assumed or identified ground acceleration. These modal parameters further lead to the estimation of the building's structural parameters when the mass properties of the building are known. The second technique then estimates the ground acceleration using the absolute acceleration and the obtained structural parameters from the first technique. The two techniques are performed iteratively until the estimated structural parameters converge. A numerical example and a laboratory test are used to illustrate the proposed identification method. Results show that the estimation of structural parameters is fairly robust to the presence of measurement noise while the unknown ground acceleration is not in high frequency range. Factors influencing the performance of the technique are also studied and discussed.