  We construct a new off-shell $\mathcal{N}{=}4$, $d{=}3$ nonlinear vector
supermultiplet. The irreducibility constraints for the superfields leave in
this supermultiplet the same component content as in the ordinary linear vector
supermultiplet. We present the most general sigma-model type action for the
$\mathcal{N}{=}4$, $d{=}3$ electrodynamics with the nonlinear vector
supermultiplet, which despite the nonlinearity of the supermultiplet may be
written as an integral over a chiral superspace. This action share the most
important properties with its linear counterpart. We also perform the
dualization of the vector component into a scalar one and find the
corresponding $\mathcal{N}{=}4$, $d{=}3$ supersymmetric action which describes
new hyper-K\"ahler sigma-model in the bosonic sector.
