Inelastic neutron scattering measurements on Ba(Fe0.963Ni0.037)2As2 manifest a neutron spin resonance in the superconducting state with anisotropic dispersion within the Fe layer. Whereas the resonance is sharply peaked at the antiferromagnetic (AFM) wave vector Q(AFM) along the orthorhombic a axis, the resonance disperses upwards away from Q(AFM) along the b axis. In contrast to the downward dispersing resonance and hourglass shape of the spin excitations in superconducting cuprates, the resonance in electron-doped BaFe2As2 compounds possesses a magnonlike upwards dispersion.