The definitive geomagnetic reference field (DGRF) models for 1965, 1970, and 1975 and the international geomagnetic reference field (IGRF) model for 1980 with linear interpolation between the four epochs is defined as the DGRF linear model. It has 480 spherical harmonic coefficients. This model contains a piecemeal linear representation of coefficients, and hence of the field itself, that results in discontinuities in the secular variation which may lead to difficulties if the model is used at different epochs to subtract values from observations to obtain anomaly fields. A new DGRF cubic model is defined by the coefficients of a cubic curve for the time dependence of each spherical harmonic coefficient. It exactly fits the DGRF linear model coefficients at 1965, 1970, 1975, and 1980 and has continuous first, second, and third derivatives throughout the interval 1965-1980. This DGRF cubic model also contains 480 coefficients which can replace the 480 coefficients of the DGRF linear model. Differences in field components computed using the two models for epochs between the key epochs of the DGRF linear model are considerable, amounting to over 60 nT in 1977.5 for the Z component. No significant differences were found in the comparison of the two models with observatory data. This comparison is difficult because of observatory anomaly biases which appear to be variable with time because of observatory measurement errors or inadequate models. Because the DGRF cubic model provides a model of continuous secular variation, it is recommended that it replace the DGRF linear model.