The middle-aged supernova remnant ( SNR ) CTB 37A is known to interact with several dense molecular clouds through the detection of shocked { H _ { 2 } } and OH 1720 MHz maser emission . In the present work , we use eight years of \textit { F } ermi -LAT Pass 8 data , with an improved point-spread function and an increased acceptance , to perform detailed morphological and spectral studies of the \gamma -ray emission toward CTB 37A from 200 MeV to 200 GeV . The best fit of the source extension is obtained for a very compact Gaussian model with a significance of 5.75 \sigma and a 68 % containment radius of 0 \fdg 116 \pm 0 \fdg 014 _ { stat } \pm 0 \fdg 017 _ { sys } above 1 GeV , which is larger than the TeV emission size . The energy spectrum is modeled as a LogParabola , resulting in a spectral index \alpha = 1.92 \pm 0.19 at 1 GeV and a curvature \beta = 0.18 \pm 0.05 , which becomes softer than the TeV spectrum above 10 GeV . The SNR properties , including a dynamical age of 6000 yr , are derived assuming the Sedov phase . From the multiwavelength modeling of emission toward the remnant , we conclude that the nonthermal radio and GeV emission is mostly due to the reacceleration of preexisting cosmic rays ( CRs ) by radiative shocks in the adjacent clouds . Furthermore , the observational data allow us to constrain the total kinetic energy transferred to the trapped CRs in the clouds . Based on these facts , we infer a composite nature for CTB 37A to explain the broadband spectrum and to elucidate the nature of the observed \gamma -ray emission .