Conventional printer characterisation models are generally based on the assumption that the densities of primary colours are additive. However, additivity failure frequently occurs in practice. We propose a novel grey component replacement (GCR) method based on the spectral density sub-additivity equations in this letter for spectral characterisation of a 4-ink colour printer. The method effectively correct the error caused by additivity failure. Real high-quality hardcopy samples are produced as evidence of the feasibility of the proposed method and to evaluate the model performance. Finally, the GCR model for characterising colour printer with high spectral and colorimetric prediction accuracy is established.