To overcome the "spurious" association caused by population stratification in population-based association studies, we propose a principal-component based method that can use both family and unrelated samples at the same time. More specifically, we adapt the multivariate logistic model, which is often used in segregation analysis and can allow for the family correlation structure, for association analysis. To correct the effect of hidden population structure, the first ten principal-components calculated from the matrix of marker genotype data are incorporated as covariates in the model. To test for the association, the marker of interest is also incorporated as a covariate in the model. We applied the proposed method to the second generation (i.e., the Offspring Cohort), in the Genetic Analysis Workshop 16 Framingham Heart Study 50 k data set to evaluate the performance of the method. Although there may have been difficulty in the convergence while maximizing the likelihood function as indicated by a flat likelihood, the distribution of the empirical p-values for the test statistic does show that the method has a correct type I error rate whenever the variance-covariance matrix of the estimates can be computed.