Two methods are typically used for the analysis of multivariate longitudinal data: multivariate random-effects growth curve models and latent curve models. Despite their popularity, in the former method an entire set of basis functions should a priori be specified and in the latter the estimates of random-effects or latent variable scores are not uniquely determined. An extended multivariate random-effects growth curve model is proposed to overcome the limitations of the two methods. The proposed method extends the existing multivariate random-effects growth curve model in such a way that it does not need to specify all basis functions in advance. It also offers the unique estimates of random-effects. Furthermore, the method can deal with unbalanced response variables, so that they do not have to be measured at the same time points, nor the same number of time points. An example is given to illustrate the method.