Response surface methodology was employed to investigate the effects of drying temperature (15.0–45.0C), air velocity (1.00–2.00 m/s), moisture content at conversion point (40.0–60.0%) and microwave (MW) power (1.0–3.0 W/g) on the average drying rate (DR), specific moisture evaporation rate (SMER), total color difference (ΔE), rehydration ratio (RR) and shrinkage ratio (SR) of yacon dried by combined heat pump (HP) and MW methods. A central composite rotatable design was used to develop models for responses. The coefficients of determination R2 of DR, SMER and ΔE were higher than 0.7. However, R2 of RR and SR were 0.540 and 0.343, respectively. Based on response surface and desirability functions, the optimum conditions for combined HP and MW drying of yacon were drying temperature of 42.7C, air velocity of 1.69 m/s, moisture content at conversion point of 50% and MW power of 2.0 W/g. At this optimum point, DR, SMER and ΔE were 0.262 kgH2O/kg(d.b.)·h, 0.222 kg/kW·h and 23.59, respectively. Practical Applications Yacon are rich in essential amino acids, minerals and fructooligosaccharides (FOS). However, FOS hydrolyzation, browning and decay are the common phenomena during postharvest storage and transportation. Hybrid drying techniques are being developed to minimize weakness and maximize merits of different drying techniques to produce better quality of foodstuffs, reduce drying time, decrease energy consumption and increase drying efficiency. Therefore, response surface methodology was employed to investigate the effects of drying temperature, air velocity, moisture content at conversion point and MW power on the average DR, SMER, ΔE, RR and SR of yacon dried by combined HP and MW methods, and the optimum process conditions were determined to obtain the criteria of maximum DR and SMER, and minimum ΔE. This research will provide valuable information for industrialization of yacon dried by combined HP and MW methods.