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We independently determine the zero-point offset of the Gaia early DataRelease-3 (EDR3) parallaxes based on $\sim 110,000$ W Ursae Majoris (EW)-typeeclipsing binary systems. EWs cover almost the entire sky and are characterizedby a relatively complete coverage in magnitude and color. They are an excellentproxy for Galactic main-sequence stars. We derive a $W1$-band Period-Luminosityrelation with a distance accuracy of $7.4\%$, which we use to anchor the Gaiaparallax zero-point. The final, global parallax offsets are $-28.6\pm0.6$$\mu$as and $-25.4\pm4.0$ $\mu$as (before correction) and $4.2\pm0.5$ $\mu$asand $4.6\pm3.7$ $\mu$as (after correction) for the five- and six-parametersolutions, respectively. The total systematic uncertainty is $1.8$ $\mu$as. Thespatial distribution of the parallax offsets shows that the bias in thecorrected Gaia EDR3 parallaxes is less than 10 $\mu$as across $40\%$ of thesky. Only $15\%$ of the sky is characterized by a parallax offset greater than30 $\mu$as. Thus, we have provided independent evidence that the parallaxzero-point correction provided by the Gaia team significantly reduces theprevailing bias. Combined with literature data, we find that the overall GaiaEDR3 parallax offsets for Galactic stars are $[-20, -30]$ $\mu$as and 4-10$\mu$as, respectively, before and after correction. For specific regions, anadditional deviation of about 10 $\mu$as is found.

Gaia EDR3 Parallax Zero-point Offset based on W Ursae Majoris-type Eclipsing Binaries