In the analysis of clustered survival data arising from family-based studies with missing covariates, current multiple imputation (MI) methods do not handle the hierarchical structure of the data and the ascertainment of families. Especially when the time-to-event and the proband information in a genomics study should be conditioned when sampling the missing data distribution. We propose a Monte Carlo Expectation Maximization (MCEM) method and further adapt it into an MI method considering the family structure and the proband information using kinship matrix. Through simulations of family-clustered survival data with covariates missing at random (MAR) and an application to breast cancer families recruited from the Breast Cancer Family Registries with missing PRS and mutation gene status, our study aims to evaluate the effectiveness of the proposed method by comparing its performance to a complete case analysis.