Laser-driven deuterons generate neutrons with a mean energy of 2.5 MeV, through the 2H(d,n) fusion reaction in a deuterated polyethylene (dPE) tablet. The deuterium ions are accelerated by 12 fs, 21 mJ laser pulses interacting with a 0.2 µm thin dPE foil at a peak intensity of 1018 W/cm2. The laser was operated at 1 Hz repetition rate in bursts of 75 shots. The interaction was characterized and recorded for each laser shot. The ion spectra were measured in the forward and backward directions by Thomson ion spectrometers. Neutron events were detected by a time-of-flight (ToF) system consisting of four plastic scintillators positioned at various angles around the experimental chamber. The maximum cut-off energy of the forward accelerated protons and deuterons was close to 1.4 MeV and 1 MeV, while the mean values are 428 ± 63 keV and 433 ± 80 keV, respectively. Analysis of ToF distributions from 3128 shots resulted in an average yield of 1142 ± 59 neutrons per shot in the energy range of 1.5–4 MeV. The energy distribution of forward-directed neutrons peaks between 3 and 3.5 MeV. Angular dependence analysis showed a perpendicular minimum and a maximum along the deuteron beam, consistent with the expected distribution from the literature and our simulation results.