We present an X-ray study of the mixed-morphology supernova remnant CTB 1 (G116.9+0.2) observed with Suzaku. The 0.6-2.0 keV spectra in the northeast breakout region of CTB 1 are well represented by a collisional ionization-equilibrium plasma model with an electron temperature of ~ 0.3 keV, whereas those in the southwest inner-shell region can be reproduced by a recombining plasma model with an electron temperature of ~ 0.2 keV, an initial ionization temperature of ~ 3 keV, and an ionization parameter of ~ 9 $times$ 10$^{11}$ cm$^{-3}$s. This is the first detection of the recombining plasma in CTB 1. The electron temperature in the inner-shell region decreases outwards, which implies that the recombining plasma is likely formed by the thermal conduction via interaction with the surrounding cold interstellar medium. The Ne abundance is almost uniform in the observed regions whereas Fe is more abundant toward the southwest of the remnant, suggesting an asymmetric ejecta distribution. We also detect a hard tail above the 2 keV band that is fitted with a power-law function with a photon index of 2-3. The flux of the hard tail in the 2-10 keV band is ~ 5 $times$ 10$^{-13}$ erg cm$^{-2}$ s$^{-1}$ and is peaked at the center of CTB 1. Its origin is unclear but one possibility is a putative pulsar wind nebula associated with CTB 1.