  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. It is found that their values calculated with $m_q$=420 MeV and
$\Lambda_N$=1.25 GeV agree very well with the experimental data. It is turned
out that the electric proton and magnetic nucleon form factors fall faster than
the dipole fit of the experimental data for momentum transfers $0\le Q^2\le 1$
GeV$^2$.
