An application of a new generalized Bayesian binary regression cohort model revealed interesting fact about contraceptive behavior of Bangladeshi women. Many women prefer to avoid their childbirth but nevertheless are not using any method of contraceptive. They are said to have an Unmet Need for Contraception (UNC). Increases in contraceptive prevalence and declines in fertility could be achieved by first eliminating unmet need. Our model not only helps to see the effects of age, period and cohort but also to explore the influence of the covariates on unmet need for contraception as well. The best model is chosen among twenty-six models fitted to the data by Akaike Bayesian Information Criterion (ABIC). The model indicates that women in the younger cohorts are more conscious about the number of living children than older cohorts, and the field workers' visit is increasing its efficiency.