•A new nonlinear fatigue damage accumulation model based on isodamage curves.•A damage function related to isodamage curves and remaining life aspects.•Fatigue damage modelling and life prediction considering the influence of loading history.•Proposed model yields better predictions of three materials under eight types of load spectra than others. Cumulative fatigue damage analysis and life prediction of engineering structures/components is vital for ensuring their structural integrity and operational reliability under variable amplitude loadings. In this regard, a new nonlinear fatigue damage accumulation model is proposed by introducing a damage function related to the isodamage curves and remaining life aspects. Specifically, its damage exponent is refined by considering effects of loading history. Experimental data from tests available in literature are utilized for model validation and comparison. Compared with four existing models, the proposed model shows higher precision for cumulative damage modelling and fatigue life prediction than others. Moreover, it improves the deficiencies inherent in other rules under the promise of maintaining its simplicity in practice.