An experiment to search for double β (2β) decay of ¹⁰⁶Cd with the help of a low-background cadmium tungstate crystal scintillator developed from cadmium enriched in ¹⁰⁶Cd to 66 % (106CdWO4, 215 g) is in progress at the STELLA facility of the Gran Sasso underground laboratory (INFN, Italy). The ¹⁰⁶CdWO₄ scintillator is viewed by low-background photomultiplier through a PbWO₄ crystal light-guide produced from deeply purified archaeological lead. The detector operates in coincidence with the four low-background HPGe detectors to search for 2β processes with the emission of gamma quanta. Sensitivity of the experiment after 10678 h of data taking to different channels of 2β decay of ¹⁰⁶Cd is on the level of limT₁/₂ ~ 10¹⁹-10²¹ years.