Longitudinal biomarkers are commonly collected in many observational studies and clinical trials. Dynamic disease risk prediction based on updated longitudinal biomarkers is of increasing interest to both researchers and medical practitioners. In this paper, we propose a novel conditional modeling approach for dynamic risk prediction of a survival outcome using longitudinal biomarkers. The idea is to factor the joint density of the biomarkers and the survival time into the product of a conditional density of the biomarkers given the survival time and a marginal density of the survival time, so that the conditional density of the survival time given the biomarkers can be derived. To model the biomarkers conditional on the survival time, we propose a nonlinear mixed model that treats the survival time as an additional covariate via a smooth or a latent changepoint kernel function to account for its effects. The t-year absolute risk prediction and the associated asymptotic variance are derived under two different assumptions for the censoring time. Compared with existing risk prediction methods, such as the joint modeling and the landmark approaches, the proposed conditional modeling approach makes less strict model assumptions, and hence has more robust predictive performance, as demonstrated by the simulation studies. The proposed approach was motivated by and applied to the ovarian cancer risk prediction in the National Cancer Institute Prostate, Lung, Colorectal, and Ovarian (PLCO) Cancer Screening Trial.