This paper investigates the strength and failure mechanisms of interphase in a carbon fibre/polyetheretherketone (PEEK) matrix composite which are affected by the cooling rate from the moulding temperature. The interphase properties are characterised using the single fibre pull-out test and short-beam shear test. The pull-out processes and fracture surface of composites are in situ evaluated under an optical microscope and a scanning electron microscope (SEM), respectively. A slow cooling rate results in a high degree of crystallinity and high modulus of the matrix, leading to a high interfacial shear strength (IFSS) along with prevailing brittle interface fracture. An amorphous dominant matrix is developed at high cooling rates, resulting in relatively low IFSS due to the interphase shear deformation. The interlaminar shear strength (ILSS) is roughly proportional to the IFSS with respect to cooling rate, although the absolute values are 20 similar to 30\% lower for the former than the latter, Both the IFSS and ILSS become insensitive once the cooling rate is higher than about 500degreesC/min, while the degree of crystallinity continues to decrease with cooling rate. The implications of fracture surfaces arc presented with regard to the interface failure mechanisms due to the change of the cooling rate.