The underlying principle behind structural damage detection techniques is that vibration signature, e.g. modal properties or frequency response function (FRF) data, is a sensitive indicator of structural physical integrity and thus can be used to detect damage. Since indirectly-measured modal data contain accumulative errors incurred in modal parameter extraction and provide much less information than FRF data, it is more reasonable and reliable to use directly-measured FRF data for structural damage detection In this paper, a new damage detection algorithm is formulated to utilize an original analytical model and FRF data measured prior and posterior to damage for structural damage detection. Based on nonlinear perturbation equations of FRF data, an algorithm has been derived which can be used to determine a damage vector indicating both location and magnitude of damage from perturbation equations of FRF data. An additional development with respect to the proposed technique is an effective technique introduced for weighting perturbation equations of FRF data at selected locations and frequencies so as to reduce influence of measurement errors on accuracy of damage detection to the minimum. For extension of the proposed algorithm to cases of incomplete measurement in terms of coordinates, an iterative version of the proposed algorithm has been introduced. The validity and applicability of the proposed damage detection algorithm have been demonstrated through numerical and experimental studies on a practical plane 3-bay frame structure, respectively.