The problem of acoustic-to-articulatory speech inversion continues to be a challenging research problem which sig- nificantly impacts automatic speech recognition robustness and accuracy. This paper presents a multi-task kernel based method aimed at learning Vocal Tract (VT) variables from the Mel-Frequency Cepstral Coefficients (MFCCs). Unlike usual speech inversion techniques based on individual esti- mation of each tract variable, the key idea here is to consider all the target variables simultaneously to take advantage of the relationships among them and then improve learning per- formance. The proposed method is evaluated using synthetic speech dataset and corresponding tract variables created by the TAsk Dynamics Application (TADA) model and com- pared to the hierarchical ε-SVR speech inversion technique.