The lightest electroweak baryon as a topological object is investigated by using a general effective Lagrangian of composite electroweak symmetry breaking and the spin-independent electroweak baryon-nucleon scattering cross section is calculated. We explicitly show the masses of the electroweak baryons and the cross section as functions of the Peskin-Takeuchi $S$ parameter and the ratio of the masses of axial-vector and vector composite bosons. We find that it is acceptable to regard the electroweak baryon as a dark matter candidate and the even number of technicolor is favored. ; Comment: 6 pages, 5 figures. Comments are Welcome