This paper presents a novel algorithm for independent vector analysis (IVA) of Gaussian data sets. Following a maximum likelihood (ML) approach, we show that the cost function to be minimized by the proposed GML-IVA algorithm reduces to an estimate of the mutual information among the different sets of latent variables. The proposed method, which can be seen as a new generalization of canonical correlation analysis (CCA), is based on the sequential solution of different least squares problems obtained from the quadratic approximation of the non-convex IVA cost function. The convergence and performance of the proposed algorithm are illustrated by means of several simulation examples, including an application consisting in the joint blind source separation (J-BSS) of three color images.