As one of the standard and fundamental weapons in the functional linear regression, the functional principal component regression (PCR) could fail to offer a good prediction provided that the response is highly correlated with some excluded functional principal component(s). This awkward situation is far from rare since the construction of functional principal components never involves the information of response. Aiming at this notorious shortcoming, we develop the functional continuum regression (CR). What distinguishes it is the intriguing inclusion property: the framework of functional CR embraces more than the functional PCR and functional partial least squares and, as the consequence, is expected to improve the prediction accuracy of the latter two approaches. This conjecture is partially supported by the competitive performance of functional CR in the application onto two representative sets of real data as well as corresponding comparison with other existing methods.