  We report the calculation of electromagnetic form factors of nucleons within
a relativistic three-quark model with Gaussian shape for the nucleon-quark
vertex. The allowed region for two adjustable parameters, the range parameter
$\Lambda_N$ in the Gaussian and the constituent quark mass $m_q$, is obtained
from fitting the data for magnetic moments and electromagnetic radii of
nucleons. The shapes of electric and magnetic nucleon form factors calculated
in this approach with the central parameters $m_q$=420 MeV and $\Lambda_N$=1.25
GeV are close to the data for momentum transfers $0\le Q^2\le 1$ GeV$^2$
