Solid state fermentation (SSF) process represents a technological alternative for a great variety of legumes and cereals, or combination of them, to improve their nutritional quality and to obtain edible products with palatable sensorial characteristics. The objectives of this work were (1) to determine the best combination of SSF process variables (temperature/time) for production of quality protein maize ( Zea mays L.) (QPM) tempeh flour, and (2) to characterize physico-chemical properties and nutritionally quality of optimized QPM tempeh flour. Response surface methodology (RSM) was applied as optimization technique, over three response variables: In vitro protein digestibility ( PD), true protein ( TD) and water absorption index ( WAI). A central composite experimental design with two factors [fermentation temperature ( FT), fermentation time ( Ft)] and five levels (2 factorial, 2 axial, 1 central) was used. The process variables, FT and Ft, had variation levels of 31–36°C and 48–72 h, respectively. Spores from Rhizopus oligosporus were suspended in distilled water (1×10 6 spores/ml) and used as starter. Predictive models for response variables were developed as a function of process variables. Conventional graphical method was applied to obtain maximum PD, TP and WAI. Contour plots of each of the response variables were utilized, applying superposition surface methodology, to obtain a contour plot for observation and selection of the best combination of FT (35.4°C) and Ft (54.6 h) for production of QPM tempeh, which was dried (52°C, 24 h) and milled to pass through a 80-US mesh (0.180 mm) screen to obtain optimized QPM tempeh flour. This flour had higher ( p⩽0.05) true protein (13.1 vs 9.1 g/100 g, DM), total colour difference (21.7 vs 9.2), WAI (2.9 vs 1.25 g gel/g dry flour), available lysine (5.67 vs 4.2 g lysine/100 g protein) and PD (83.6 vs 78.5%, DM), and lower ( p⩽0.05) lipid content (4.3 vs 6.1 g/100 g, DM), phytic acid (0.8 vs 10.1 mg phytic acid/g, DM), and pH (4.5 vs 6.12) than raw QPM flour.