Independent component analysis (ICA) is a statistical and computational technique for revealing hidden factors that underlie sets of signals. We propose an improved ICA framework for group data analysis by adding an adaptive constraint to the mixing coefficients, namely, constrained coefficients ICA (CCICA). The method is dedicated to identification and increasing the accuracy of components that show significant group differences reflected in the mixing coefficients. Performance of CCICA is assessed by simulations under different signal to noise ratios. An application to multitask functional magnetic resonance imaging analysis is conducted to illustrate the advantages of CCICA. It is shown that CCICA provides stable results and can estimate both the components and the mixing coefficients with a relatively high accuracy compared to Infomax, hence is a promising tool for the identification of biomarkers from brain imaging data.