A time-based fatigue crack growth algorithm is proposed in this paper to calculate the fatigue crack growth under general random variable amplitude loading. This approach is based on the analytical crack tip opening displacement (CTOD) estimation and a subcycle fatigue crack growth model. The discussion is first given for fatigue cracks without considering the crack closure. Next, the model is extended to the growing crack with the crack closure. Following this, a general fatigue crack growth algorithm is proposed under general random variable loadings, which is combined the crack closure model and the geometrical relationship between the CTOD and the crack increment (da) at any time instant within a cycle. To validate this algorithm, a testing is performed for Al7075-T6 under "Christmas Tree" loading spectra, which cannot be easily handled by the classical cycle-based approaches. The predictions match the experimental data very well. A detailed discussion is given based on the current investigation.