The aim of this paper is to develop a class of linear mixed effects models with functional covariates (LMMFC). This development is motivated by the use of neuroimaging marker(s) to predict longitudinal clinical outcomes. A total variation penalty is introduced to characterize slope image(s) associated with the functional covariates in LMMFC. An Alternating Direction Method of Multipliers (ADMM) algorithm is proposed to simultaneously estimate the slope image and other unknown parameters, such as variance components in LMMFC. Theoretically, we establish an upper bound for the estimation error and prove the consistency of the variance component estimates. We also develop a bootstrap test procedure to carry out a global significance test for the slope image. Our simulations demonstrate a superior performance of LMMFC over many existing approaches. We use LMMFC to predict clinical scores by using a hippocampus covariate obtained from the Alzheimers Disease Neuroimaging Initiative (ADNI) study.