Long‐period zonal tidal Love numbers are more sensitive to lower‐mantle anelasticity (which is difficult to determine even from laboratory); however, the Love numbers of the zonal tides have not been adequately determined. In this study, we use the optimal sequence estimation method with the Global Positioning System (GPS) displacements to estimate the complex Love numbers of the long‐period zonal tides. For the first time, we retrieve the complex Love numbers h20 and l20 for the Msm, Msf, SN, Mstm, Mtm, Msqm, and Mqm tides from the Up‐ and North‐components of the global GPS displacements; we also re‐estimate the same complex Love numbers for the Mm (monthly) and Mf (fortnightly) tides with a higher precision. Based on the robust estimated h20 and l20 values for the nine zonal tides, we inverse their corresponding mantle anelastic parameters fr and fi, respectively. We finally obtain that the material‐dependent parameter α for the lower mantle is 0.189 ± 0.07, and find that the 18.6‐year nodal tide and the Chandler wobble, as well as the long‐period zonal tides, can be represented by a single absorption band. Our estimates for fr, fi, and α can be further used to construct attenuation and velocity models of the Earth's interior. Plain Language Summary: As the Earth is an anelastic body, the observed Earth tides will have different amplitudes from the theoretical tides for a perfectly elastic Earth model. The differences can be scaled by the Love numbers, k, h, and l. The Global Positioning System (GPS) displacements are affected by the Sun and Moon, and hence can record the tides. If we can separate different tidal signals, we can compare the observed signals with the theoretical signals from an elastic Earth model, and hence obtain the corresponding Love numbers. The long‐period zonal tides are only related to the spherical harmonic Y20, so here we use a special method, the optimal sequence estimation method, to isolate nine Y20‐related zonal tides from the global GPS displacement observations, and finally obtain their corresponding Love numbers h20 and l20. Among them, the results for the Msm, Msf, SN, Mstm, Mtm, Msqm, and Mqm tides are obtained for the first time, and the results for the Mm and Mf tides are estimated with higher precision. Based on those new estimated Love numbers, we further estimate the mantle anelastic parameters fr and fi. Finally, we confirm that those nine zonal tides can be represented by a single absorption with α = 0.189 ± 0.07. Key Points: The optimal sequence estimation method is used to retrieve the Love numbers of nine zonal tides from global Global Positioning System displacementsWe estimate the Love numbers h20 and l20 of seven zonal tides and re‐estimate those of the fortnightly and monthly tides with higher precisionMantle anelasticity is estimated from nine zonal tides for the first time; the final estimated material‐dependent value α = 0.189 ± 0.07 [ABSTRACT FROM AUTHOR]