A generalized least squares lattice algorithm (GLSLA), which is appropriate for multi-channel adaptive filtering and estimation, is presented. This algorithm has all the advantages of a conventional least-squares (LS) lattice algorithm, such as computational efficiency, numerical stability, and the property that successive stages are decoupled. Besides these advantages, it also has the flexibility that the number of stages in each channel may be different. This property does not exist in the conventional LS lattice algorithms. As an application, a decision feedback equalizer (DFE) with different numbers of feedforward and feedback stages is proposed and implemented using the GLSLA. Some results obtained from a computer simulation of the algorithm are also presented.