The cause-specific cumulative incidence function (CIF) quantifies the subject-specific disease risk with competing risks. With longitudinally collected biomarker data, it is of interest to dynamically update the predicted CIF by incorporating the most recent biomarker as well as the cumulating longitudinal history. Motivated by a longitudinal cohort study of chronic kidney disease, we propose a framework for dynamic prediction of end stage renal disease using multivariate longitudinal biomarkers, accounting for the competing risk of death. The proposed framework extends the landmark survival modeling to the competing risks data, and implies a distinct sub-distribution hazard regression model defined at each landmark time. The model parameters, prediction horizon, longitudinal history and at-risk population are allowed to vary over the landmark time. When the measurement times of biomarkers are irregularly spaced, the predictor may not be observed at the time of prediction. Local polynomial is used to accommodate this situation and estimate the model parameters without explicitly imputing the predictor or modeling its longitudinal trajectory. The proposed model leads to simple interpretation of the regression coefficients and closed-form calculation of the predicted CIF. The estimation and prediction can be implemented through standard statistical software, with tractable computation. We conducted simulations to evaluate the performance of the estimation procedure and predictive accuracy. The methodology is illustrated with data from the African American Study of Kidney Disease and Hypertension.