  In this paper, we generalize a boundary state to the one incorporating
non-constant gauge field strength as an external background coupled to the
boundary of a string worldsheet in bosonic string theory. This newly defined
boundary state satisfies generalized nonlinear boundary conditions with
non-constant gauge field strength, and is BRST invariant. The divergence
immanent in this boundary state coincide with the one calculated in a string
sigma model. We extract the relevant massless part of this generalized boundary
state, and give a part of the D-brane action with the non-constant gauge field
strength, that is, derivative corrections to the D-brane action.
