Abstract We report results of a search for galaxies at z > 3 with Lyman continuum (LyC) emission using a narrow-band filter NB359 with Subaru/Suprime-Cam in an ∼800 arcmin2 blank field around the GOODS-N. We use 103 star-forming galaxies (SFGs) and 8 active galactic nuclei (AGNs) with spectroscopic redshifts in a range between 3.06 and 3.5 and 157 photometrically selected z = 3.1 Lyman α emitter (LAE) candidates as the targets. After removing galaxies spectroscopically confirmed to be contaminated by foreground sources, we found two SFGs and one AGN as candidate LyC-emitting sources among the targets with spectroscopic redshifts. Among LAE candidates, five sources are detected in the NB359 image, and three among them may be contaminated by foreground sources. We compare the sample galaxies in the GOODS-N with those in the SSA22, where a prominent protocluster at z = 3.1 is known and an LyC search using the same NB359 filter has been made. The frequency of galaxies with LyC leakage in the SSA22 field may be about two times higher than that of galaxies in the GOODS-N with the sample ultraviolet (UV) magnitude range, although the numbers of LyC detections in these fields are too small to make a statistically significant conclusion. By combining the sample galaxies in these fields, we place the 3σ upper limits of the observed LyC-to-UV flux density ratio and LyC escape fraction for galaxies at z = 3.1 with absolute UV magnitude MUV < −18.8 as (fLyC/fUV)obs < 0.036 and $f_\mathrm{esc}^\mathrm{abs}\,\lt\, 8$ per cent, respectively.