Logistic　mixed-effects　models　are　widely　used　to　study　the　relationship　between　the　binary　response　and　covariates　for　longitudinal　data　analysis,　where　the　random　effects　are　typically　assumed　to　have　a　fully　parametric　distribution.　As　this　assumption　is　likely　limited　or　unreasonable　in　a　multitude　of　practical　researches,　a　semiparametric　Bayesian　approach　for　relaxing　it　is　developed　in　this　paper.　In　the　context　of　binomial　distribution　logistic　mixed-effects　models,　a　general　Bayesian　framework　is　presented　in　which　a　semiparametric　hierarchical　modelling　with　an　approximate　truncated　Dirichlet　process　prior　distribution　is　specified　for　the　random　effects.　The　stick-breaking　prior　and　the　blocked　Gibbs　sampler　using　Polya-Gamma　mixture　are　employed　to　efficiently　sample　in　the　posterior　analysis.　Besides,　a　procedure　calculating　DIC　for　Bayesian　model　comparison　is　addressed.　The　methodology　is　demonstrated　through　simulation　studies　and　a　real　example.