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Abstract With the increasing use of composite material and external energy dissipation device in civil structures, the classical Rayleigh damping becomes an inappropriate assumption in structural damage identification. In this paper, a parametric sensitivity-based approach is developed to identify the structural damage and damping defect of non-classically damped shear-type building simultaneously. As the preliminary step, the complex eigenvalues and eigenvectors of damaged structure are obtained by a novel identification technique, which decouples the first-order modal analysis equation under physical coordinate so that the complex modal parameters of each mode can be identified independently. Thereafter, by analysing the sensitivities of complex eigenparameter, non-linear least square method is applied to identify the locations and magnitudes of damage with respect to stiffness reduction and damping defect. The proposed identification approach is illustrated by identifying the damage in a numerical five-storey shear building. The identification results show that the proposed approach can locate and quantify the stiffness reductions satisfactorily even when measurement noise is taken into account. However, in order to quantify the damping defects consistently, their locations need to be known as a priori. Highlights • A novel complex eigenparameter identification approach under state-space coordinate. • Damage identification on non-proportionally damped shear-type building. • Identify the stiffness reduction and damping defect simultaneously. • Identify the design parameters which locate and quantify the damages. • Numerical validation on a five-storey shear building by considering measurement noise. [ABSTRACT FROM AUTHOR]