  We present a D-term hybrid inflation model, embedded in supergravity with
moduli stabilisation. Its novel features allow us to overcome the serious
challenges of combining D-term inflation and moduli fields within the same
string-motivated theory. One salient point of the model is the positive
definite uplifting D-term arising from the moduli stabilisation sector. By
coupling this D-term to the inflationary sector, we generate an effective
Fayet-Iliopoulos term. Moduli corrections to the inflationary dynamics are also
obtained. Successful inflation is achieved for a limited range of parameter
values with spectral index compatible with the WMAP3 data. Cosmic D-term
strings are also formed at the end of inflation; these are no longer
Bogomol'nyi-Prasad-Sommerfeld (BPS) objects. The properties of the strings are
studied.
