We explore the possible quasi-periodic oscillations (QPOs) of the blazar PKS 1510−089, utilizing the ∼38-yr Metsähovi flux density observations at 37 GHz and over 10-yr Fermi Large Area Telescope observations in the 0.1–300 GeV energy range. Both the flux distributions of the radio and γ-ray light curves suggest a lognormal distribution, and power spectral densities of both light curves can be well represented by a bending power-law model. Comparing the results from the weighted wavelet Z-transform and Lomb–Scargle periodogram approaches, a quasi-period of 1330 ± 55 d at a 99.80 per cent (>3σ) significance against the red noise background is observed in the radio light curve, whereas no similar modulation is seen in the γ-ray light curve. We briefly discuss the research actuality of blazar QPO phenomena and explain the observed radio QPO as the result of Keplerian motion in a supermassive binary black hole system and periodic modulation induced by the Lense–Thirring precession of the innermost portions of the accretion disc.