The problem of missing data prevails in medical and research studies. Ways of handling missing data can have a significant effect on the conclusions drawn from the data. So, it is important to consider the missing data mechanisms and make suitable assumptions in choosing a missing data approach. On the basis of simulated bivariate longitudinal data from a group of subjects, we explored four imputation approaches including Multiple Imputation via Chained Equations (MICE), Expectation- Maximization (EM) algorithm, fully conditional specification via univariate mixed models, and imputation via predicted means under bivariate mixed models based on complete data. The data simulation was conducted under three mechanisms: missing completely at random (MCAR), missing at random (MAR) and missing not at random (MNAR) with variety of missing proportions for each response, sample sizes, lengths of time intervals, and parameters. The performance and trade-offs of the imputation approaches were assessed in terms of Root Mean Square Errors (RMSE) on the bivariate responses, relative bias with respect to the parameters and coverage rates of the slope confidence intervals.