  MiniJPAS is a ~1 deg^2 imaging survey of the AEGIS field in 60 bands,
performed to demonstrate the scientific potential of the upcoming JPAS survey.
Full coverage of the 3800-9100 \AA range with 54 narrow and 6 broad optical
filters allow for extremely accurate photo-z, which applied over 1000s of deg^2
will enable new applications of the photo-z technique such as measurement of
baryonic acoustic oscillations. In this paper we describe the method used to
obtain the photo-z included in the publicly available miniJPAS catalogue, and
characterise the photo-z performance. We build 100 \AA resolution photo-spectra
from the PSF-corrected forced-aperture photometry. Systematic offsets in the
photometry are corrected by applying magnitude shifts obtained through
iterative fitting with stellar population synthesis models. We compute photo-z
with a customised version of LePhare, using a set of templates optimised for
the J-PAS filter-set. We analyse the accuracy of miniJPAS photo-z and their
dependence on multiple quantities using a subsample of 5,266 galaxies with
spectroscopic redshifts from SDSS and DEEP, that we find to be representative
of the whole r<23 miniJPAS sample. Formal uncertainties for the photo-z that
are calculated with the \delta\chi^2 method underestimate the actual redshift
errors. The odds parameter has the stronger correlation with |Dz|, and
accurately reproduces the probability of a redshift outlier (|Dz|>0.03)
irrespective of the magnitude, redshift, or spectral type of the sources. We
show that the two main summary statistics characterising the photo-z accuracy
for a population of galaxies (snmad and \eta) can be predicted by the
distribution of odds in such population, and use this to estimate them for the
whole miniJPAS sample. At r<23 there are 17,500 galaxies/deg^2 with valid
photo-z estimates, of which 4,200 are expected to have |Dz|<0.003 (abridged).
