Joint analysis of longitudinal and survival data has received increasing attention in the recent years, especially for AIDS. This study explores application of Bayesian joint modeling of HIV/AIDS data obtained from Bale Robe General Hospital, Ethiopia. The objective is to develop separate and joint statistical models in the Bayesian framework for longitudinal measurements and time to death event data of HIV/AIDS patients. A linear mixed effects model (LMEM), assuming homogenous and heterogeneous CD4 variances, is used for modeling the CD4 counts and a Weibull survival model is used for describing the time to death event. Then, both processes are linked using unobserved random effects through the use of a shared parameter model. The analysis of both the separate and the joint models reveal that the assumption of heterogeneous (patient-specific) CD4 variances brings improvement in the model fit. The Bayesian joint model is found to best fit to the data, and provided more precise estimates of parameters. The shared frailty is significant showing the association between the linear mixed effect (LME) and survival models.