ABSTRACT Observations provide direct evidence for a sustained decline in solar activity since the 1980s, with the minimum between solar cycles 24 and 25 (P24/25) reaching its deepest trough in the past hundred years. In response to the reduced solar modulation, low-energy (<GeV) galactic cosmic rays (GCRs) at 1 au attain historical new highs in P24/25, while anomalous cosmic rays (ACRs) show very inconsistent variations with GCRs. To better understand the long-term ACR variations, we revisit the 6.0–13.4 MeV nuc−1 oxygen measurements from the WIND/LEMT instrument over 1994–2021, with particular interests to the recent three solar minima: P22/23 (solar magnetic polarity A > 0), P23/24 (A < 0), and P24/25 (A > 0). We find that the peak ACR intensities in P24/25 are ∼20 per cent lower than those in P22/23 but ∼48 per cent above those in P23/24. Additionally, for a specified heliospheric current sheet (HCS) tilt angle, the GCR intensities in P24/25 are inferred to be significantly higher than those in P22/23 (both are in A > 0 cycles), whereas the ACR intensities in P24/25 are close to those in P22/23. These results indicate that large variability in ACRs exists not only between opposite-polarity cycles, but also between different cycles of the same polarity, and ACRs may be more sensitive to varying HCS compared to GCRs. We speculate that variations in the ACR source intensity may be a key to understanding the ACR–GCR discrepancies. This is the first time for such a long-term study being possible with the same instrument.