The galactic cosmic ray (GCR) unidirectional latitudinal gradient ( $G_{\bot }$ ) is important for the understanding of the physical mechanism of solar modulation in the three-dimensional heliosphere. This work calculates the south-north (SN) asymmetry the GCR intensity from six neutron monitor (NM) stations with different geographic locations and cutoff rigidities ( $P_{\mathrm{c}}$ ). The $P_{\mathrm{c}}$ values are divided into three groups: low $P_{\mathrm{c}}$ (1 – 5 GV) for the McMurdo and Thule NMs, medium $P_{\mathrm{c}}$ (6 – 11 GV) for the Tsumeb NM and Mexico NM, and high $P_{\mathrm{c}}$ (> 12 GV) for the Haleakala NM and Princess Sirindhorn NM. The SN GCR intensities are corrected by the secular change method and the heliospheric current sheet (HCS) tilt angle for Earth’s excursions in helio-latitudes to calculate the unidirectional latitudinal gradients ( $G_{\bot }$ ) in the course of solar rotations during the $A > 0$ (1996 – 1998 and 2015 – 2019) and $A < 0$ epochs (2004 – 2008). We find that the directions of $G_{\bot }$ are opposite to the (north-South) NS offset of the HCS. The effect of the asymmetric HCS tilt on the $G_{\bot }$ is more prominent in the $A < 0$ than in the $A > 0$ epochs. The NS asymmetry in the HCS tilt and solar wind speed simultaneously contribute to the $G_{\bot }$ throughout both magnetic polarities. When the asymmetric solar wind speed is absent, the effect of the asymmetric HCS tilt on the $G_{\bot }$ is clearly observed in the $A < 0$ epoch not in the $A > 0$ epochs, and the magnitudes of $G_{\bot }$ are proportional to the size of the offset. However, when the asymmetric HCS tilt is none, the effect of the NS asymmetric solar wind speed on $G_{\bot }$ cannot be discriminated in both magnetic polarities. The slope of the SN asymmetric GCR intensity to the asymmetric solar wind speed in the $A > 0$ (2015 – 2019) is larger than in the $A < 0$ by about 1.3 – 1.8 times. The yearly GCR asymmetric latitudinal gradients tend to depend on directions of the HCS and solar wind speed offsets rather than on the solar magnetic polarities. The rigidity and asymptotic dependences of the $G_{\bot }$ are discussed.
