In this paper, we present the results of the observations of CTB 37A obtained with the X-ray imaging spectrometer onboard the Suzaku satellite. The X-ray spectrum of CTB 37A is fitted well by two components: a single-temperature ionization equilibrium component (VMEKAL), with solar abundances, an electron temperature of kTe similar to 0.6 keV and an absorbing column density of NH similar to 3 x 1022 cm-2, and a power-law component with a photon index of G similar to 1.6. The X-ray spectrum of CTB 37A is characterized by clearly detected K-shell emission lines of Mg, Si, S and Ar. The plasma with solar abundances supports the idea that the X-ray emission originates from the shocked interstellar material. The ambient gas density and the age of the remnant are estimated to be similar to 1f-1/2 cm-3 and similar to 3 x 104f1/2 yr, respectively. The centre-filling X-ray emission, surrounded by a shell-like radio structure, and other X-ray properties indicate that this remnant could be a new member of the class of mixed-morphology supernova remnants.