Motivated by the analysis of clinical studies, we propose a generalized functional partial linear varying-coefficient model for the analysis of longitudinal data where the observation times for the response and the functional covariate as well as the scalar covariates are mismatched within subjects. We represent the functional parameter by a rich truncated tensor product penalized B-spline basis. The estimators are obtained by the local kernel-weighted estimating equations with penalties, which are proposed to deal with the asynchronous longitudinal data. We examine the consistency of the estimators, and the convergence rate of the prediction error. Meanwhile, a bootstrap hypothesis testing method is developed to test the nullity of the coefficients. Simulation studies and an analysis of a real longitudinal functional dataset from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) are used to demonstrate the performance of the proposed method.