Supernova remnants (SNRs) are believed to be one of the major sources of Galactic cosmic rays. SNR CTB 37A is known to interact with several dense molecular clouds as traced by OH 1720 MHz maser. Radio and X-ray observations of the SNR confirm a mixed-morphology classification of the remnant. The TeV γ-ray source HESS J1714-385 is positionally coincident with the SNR, though it is still not clear whether the TeV γ-ray emission originates in the SNR or a plausible pulsar wind nebula (PWN). In the present work, we use 8 years of Pass 8 Fermi-LAT data, with high capability to resolve γ-ray sources, to perform morphological and spectral studies of the γ- ray emission toward CTB 37A from 200 MeV to 200 GeV. The best fit of the source extension is obtained for a Gaussian model of 68% containment radius 0.18◦ ± 0.02◦. We also discuss several possible theoretical models to explain the broadband spectrum and to elucidate the nature of the high-energy γ-ray emission toward CTB 37A.