The internationalization of mathematics education has become an inevitable trend, and bilingual education is the booster to realize the internationalization of mathematics education. Due to the vast territory of our country, there are great differences in students' foreign language level and mathematical thinking ability in different regions and colleges, so we cannot blindly formulate a unified standard for all the mathematics courses in colleges and universities to select some mathematics courses as bilingual teaching objects. For the freshmen majoring in science and engineering, it is not realistic to choose the first-year mathematics basic courses such as advanced mathematics and linear algebra as the bilingual teaching object; it is not the best choice for the senior mathematics courses such as Function of Real Variables, Functional Analysis and Topology of Point Set, which are more difficult; it is not the best choice for the bilingual teaching object compared with analysis, Function of Complex Variables is a relatively easy mathematics course, which is the extension and supplement of higher mathematics. This book is divided into nine chapters, which systematically introduces the basic theory and methods of complex variable function, including complex number and complex variable function, analytic function, integral of complex variable function, power series representation of analytic function, Laurent expansion of analytic function and its isolated singularities, residue theory and its application, conformal mappings. This book is suitable for teachers and students of science and engineering major in colleges and universities all over the country, and can also be read and referenced by engineering and technical personnel.