ABSTRACT We report the discovery of PSR J2251−3711, a radio pulsar with a spin period of 12.1 s, the second longest currently known. Its timing parameters imply a characteristic age of 15 Myr, a surface magnetic field of 1.3 × 1013 G, and a spin-down luminosity of 2.9 × 1029 erg s−1. Its dispersion measure of 12.12(1) pc cm−3 leads to distance estimates of 0.5 and 1.3 kpc according to the NE2001 and YMW16 Galactic free electron density models, respectively. Some of its single pulses show an uninterrupted 180-deg sweep of the phase-resolved polarization position angle, with an S-shape reminiscent of the rotating vector model prediction. However, the fact that this sweep occurs at different phases from one pulse to another is remarkable and without straightforward explanation. Although PSR J2251−3711 lies in the region of the $P-\dot{P}$ parameter space occupied by the X-ray isolated neutron stars (XINS), there is no evidence for an X-ray counterpart in our Swift XRT observation; this places a 99 per cent-confidence upper bound on its unabsorbed bolometric thermal luminosity of $1.1 \times 10^{31}~(d / 1~\mathrm{kpc})^2~\mathrm{erg\, s}^{-1}$ for an assumed temperature of 85 eV, where d is the distance to the pulsar. Further observations are needed to determine whether it is a rotation-powered pulsar with a true age of at least several Myr, or a much younger object such as an XINS or a recently cooled magnetar. Extreme specimens like PSR J2251−3711 help bridge populations in the so-called neutron star zoo in an attempt to understand their origins and evolution.