We observed the stress relaxation and shape recovery of a dispersed droplet phase after application of step shear strains in a polystyrene/polycarbonate blend melt. A polystyrene makes a droplet phase in a polycarbonate matrix of higher viscosity. The orientation angle of the droplet is independent of the initial radius. The angle does not change during stress relaxation and is nearly equal to the angle given by the affine deformation. The shape recovery of the droplets leads to the decay of the relaxation modulus at long times. The stress relaxation slows down at long times for large strains, reflecting the retarded shape recovery of the droplets. Calculated time dependences of the relaxation modulus based on the rate equations by Doi and Ohta [Chem. Phys. 95, 1242-1248 (1991)] do not agree with the observed slowing down of the stress relaxation. A force balance equation developed by Cohen and Carriere [Rheol. Acta 28, 223-232 (1989)] explains the retarded shape recovery of the droplet from a prolonged ellipsoid of revolution to a sphere.