Epidemiologic evidence suggests that individuals during their prenatal development may be especially vulnerable to the effects of environmental factors such as stress that predisposes them to psychiatric disorders including alcohol use disorder (AUD) later in life. Currently, the epigenetic mechanisms of anxiety comorbid with AUD induced by prenatal stress (PRS) remain to be elucidated. Here, we examined anxiety-like and alcohol drinking behaviors in adult offspring of prenatally stressed dam (PRS-mice) using elevated plus maze, light/dark box and two-bottle free-choice paradigm. It was found that PRS-mice exhibit heightened anxiety-like behaviors and increased alcohol intake in adulthood and these behavioral deficits were associated with a significant decrease in dendritic spine density (DSD) in medial prefrontal cortex (mPFC) relative to non-stressed mice (NS mice). To determine the mechanisms by which PRS reduces DSD, we examined the expressions of key genes associated with synaptic plasticity, including activity regulated cytoskeleton associated protein (Arc), spinophilin (Spn), postsynaptic density 95 (Psd95), tropomyosin receptor kinase B (TrkB), protein kinase B (Akt), mammalian target of rapamycin (mTOR) and period 2 (Per2) in mPFC of PRS and NS mice. The mRNA levels of these genes were significantly decreased in PRS mice. Methylated DNA and chromatin immunoprecipitation studies revealed hyper DNA methylation or reduced histone H3K14 acetylation on promoters of above genes suggesting that epigenetic dysregulation may be responsible for the deficits in their expression. Findings from this study suggest that prenatal stress induced abnormal epigenetic mechanisms and synaptic plasticity-related events may be associated with anxiety-like and alcohol drinking behaviors in adulthood.