We measure the redshift-space power spectrum P(k) for the recently completed IRAS Point Source Catalogue (PSC) redshift survey, which contains 14 500 galaxies over 84 per cent of the sky with 60-μm flux ≥0.6 Jy. Comparison with simulations shows that our estimated errors on P(k) are realistic, and that systematic errors resulting from the finite survey volume are small for wavenumbers k≳ 0.03 h Mpc−1. At large scales our power spectrum is intermediate between those of the earlier QDOT and 1.2-Jy surveys, but with considerably smaller error bars; it falls slightly more steeply to smaller scales. We have fitted families of CDM-like models using the Peacock–Dodds formula for non-linear evolution; the results are somewhat sensitive to the assumed small-scale velocity dispersion σV. Assuming a realistic σV≈ 300 km s−1 yields a shape parameter Γ∼ 0.25 and normalization bσ8∼ 0.75; if σV is as high as 600 km s−1 then Γ = 0.5 is only marginally excluded. There is little evidence for any ‘preferred scale’ in the power spectrum or non-Gaussian behaviour in the distribution of large-scale power.