The structural, electronic and optical properties of Mg single doped, N single doped and different concentrations Mg-N co-doped β-Ga2O3 were studied via the first-principles calculation based on density function theory. This work aims to improve the effect of p-type β-Ga2O3doping. Five models were built including Mg single doped, N-single doped, 1 Mg-N doped, 2 Mg-N doped and 3 Mg-N doped β-Ga2O3. Among them, the model of 3 Mg-N doped β-Ga2O3 shows the most stable structure than other doped systems. In attention to, the bandgap of 3 Mg-N doped β-Ga2O3 material is the smallest. And occupied states contributed by N 2p and Mg 3s inhibit the formation of oxygen vacancies, which increases the concentration of holes. Thus, 3 Mg-N doped β-Ga2O3 system displays excellent p-type feature. Adsorption peak is obvious red-shift in 3 Mg-N doped system, and the adsorption coefficient is bigger at solar-blind region, which is ascribed to the interband electron transition from the Ga 4s, Ga 4p, Mg 3s of conduct band to O 2p, N 2p of valence band. This work will provide a theoretical guide for the study and application of p-type β-Ga2O3 materials.