A novel nonlinear directional coupler consisting of tapered and uniform waveguides with self-focusing or self-defocusing nonlinear material is proposed to improve all-optical switching characteristics. Its switching characteristics are analyzed by using a beam propagation method based on the Galerkin's finite element technique (FE-BPM), in which nonuniform sampling spacings along the transverse coordinate are adopted. It is presented that the tapered nonlinear directional coupler shows fairly distinct 'high' and 'low' states of output power with steep transition versus input power. This property is discussed in comparison with conventional nonlinear directional couplers consisting of uniform symmetric and uniform asymmetric coupled waveguides. In addition, the effects of loss on the characteristics of tapered nonlinear directional coupler are examined.