Stock market integration with efficiency is important in finance. This study therefore analyses the stock market efficiency in Vietnam and other Asian countries by using the recently developed Generalized Autoregressive Conditional Heteroscedasticity (GARCH)-based unit root test of Narayan et al. to examine the stock market efficiency of Vietnam and other 18 Asian countries, using daily prices. Particularly, we examine weather stock market prices in these countries reflects all available information. The model flexibly accounts for heteroskedasticity and two structural breaks, the presence of which can lead to inaccurate results if neglected. Our results disclose the stock markets of 14 countries as inefficient following the rejection of the unit root null hypothesis. However, the stock markets of China, Hong Kong, Japan, and the Korea Republic are adjudged efficient. We further extend the model to accommodate a maximum of five breaks to check the robustness of our results to higher breaks. We observe that the results are largely consistent except for Lebanon and Singapore. For completeness, we compare the results with those of conventional GARCH models that do not account for structural breaks and discover differing results for some countries. Hence, the role of structural breaks is not negligible in assessing market efficiency. Future studies should also incorporate heteroskedasticity and structural breaks in their modelling framework to obtain accurate results.