How can I measure the mass of eclipsing binary stars? Is there any method to measure the mass of eclipsing binaries without using Doppler shift effect?
It depends.

For many categories of stars, it is possible to determine the approximate mass of the star from its non-redshifted spectrum. Stars on the main sequence: this table of spectral classifications lists the approximate mass for the various classifications. A more precise mass estimation should be possible with a more precise classification. Sol, for example, is a G2, near the high end of G, putting it near the top end of the range (0.80 - 1.04 stellar masses).