  We study the instanton calculus for N=4 super Yang-Mills theory in
ten-dimensional Omega-background with the R-symmetry Wilson line gauge field.
From the ADHM construction of instantons in the background, we obtain the
deformed instanton effective action. For a certain case we get the effective
action of N=2^* theory in the Omega-background. We also study the low-energy
effective D(-1)-brane action for the D3/D(-1)-brane system in the R-R 3-form
field strength backgrounds and find that the action agrees with the instanton
effective action in the Omega-background.
