Supernova remnants (SNRs) are considered one of the best candidates to accelerate the bulk of Galactic cosmic rays. Studying gamma-ray emission from young SNRs allows us to understand the nature of accelerated particles and the maximum energy they can reach. The SNR G150.3+4.5 was detected in radio and exhibits a shell-like morphology with an angular size of 3°, suggesting either an old or a nearby SNR. We present a spectro-morphological analysis of G150.3+4.5 with Fermi-LAT data that reveals emission up to hundreds of GeV. We estimate the distance and the surrounding density of the SNR to understand its evolutionary stage. We find that G150.3+4.5 is spectrally similar to the young shell-type SNRs observed with the Fermi-LAT such as RX J1713.7$-$3946 or Vela Junior. The broadband nonthermal emission of G150.3+4.5 is explained by a leptonic scenario that implies particle acceleration at least up to TeV energies, making G150.3+4.5 a new dynamically young SNR.