The Crab nebula is a supernova remnant exhibiting a highly polarized synchrotron radiation at radio and millimetre wavelengths. It is the brightest source in the microwave sky with an extension of 7 by 5 arcmin, and is commonly used as a standard candle for any experiment which aims to measure the polarization of the sky. Though its spectral energy distribution has been well characterized in total intensity, polarization data are still lacking at millimetre wavelengths. We report in this paper high resolution observations (18′′ FWHM) of the Crab nebula in total intensity and linear polarization at 150 GHz with the NIKA camera. NIKA, operated at the IRAM 30 m telescope from 2012 to 2015, is a camera made of Lumped Element Kinetic Inductance Detectors (LEKIDs) observing the sky at 150 and 260 GHz. From these observations we are able to reconstruct the spatial distribution of the polarization degree and angle of the Crab nebula, which is found to be compatible with previous observations at lower and higher frequencies. Averaging across the source and using other existing data sets we find that the Crab nebula polarization angle is consistent with being constant over a wide range of frequencies with a value of − 87.7° ± 0.3 in Galactic coordinates. We also present the first estimation of the Crab nebula spectral energy distribution polarized flux in a wide frequency range: 30–353 GHz. Assuming a single power law emission model we find that the polarization spectral index β_pol = – 0.347 ± 0.026 is compatible with the intensity spectral index β = – 0.323 ± 0.001.