In the development of contemporary mathematics in Vietnam complex analysis occupies a special place. We give a brief survey of the development of complex analysis in Vietnam since 1947, when the first mathematical research paper (and it was on complex analysis) written by a Vietnamese mathematician was published in an international journal. We describe how complex analysis in Vietnam developed under very special conditions: the anti-French resistance, the struggle for the reunification of the country, the American war, the economic crisis, and the change toward a market economy.