The problem of acoustic-to-articulatory speech inversion continues to be a challenging research problem which significantly 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 estimation 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 performance. The proposed method is evaluated using synthetic speech dataset and corresponding tract variables created by the TAsk Dynamics Application (TADA) model and compared to the hierarchical ε-SVR speech inversion technique.