We study thermoelectric phenomena in a system consisting of strongly correlated quantum dot coupled to external leads in the Kondo regime. We calculate linear and nonlinear electrical and thermal conductance and thermopower of the quantum dot and discuss the role of asymmetry in the couplings to external electrodes. In the linear regime electrical and thermal conductances are modified, while thermopower remains unchanged. In the nonlinear regime the Kondo resonance in differential conductance develops at non-zero source-drain voltage, which has important consequences on thermoelectric properties of the system and the thermopower starts to depend on the asymmetry. We also discuss Wiedemann-Franz relation, thermoelectric figure of merit and validity of the Mott formula for thermopower.