Inclusion Criteria:  Patients free of mental illness, able to sign consent and >18year Celiac disease confirmed by presence of serum celiac antibodies and villous atrophy on intestinal biopsy before starting gluten free diet (GFD) Intestinal villous atrophy on duodenal biopsy (performed within 1 month) showing villous atrophy Patient under GFD or starting GFD with strict compliance Hemoglobin level (Hb) <12g/dL & Hb>8g/dL Well tolerated anemia Iron deficiency defined by: serum iron level < 11 µmol/L, ferritinemia < 20µg/L and/or transferrin saturation index <0.2  Exclusion Criteria:  Patient not able to sign, mental illness, pregnancy Complicated celiac disease: intestinal malignancies Severe anemia (Hb <8g/dL) and/or poorly tolerated anemia requiring systematic iron IV supplementation or blood transfusion Serious severe disease having short-term prognostic implication Contraindication to intravenous iron infusion: known drug allergy Pregnant or breastfeeding women Participation in another interventional trial Patients treated by steroids, immunosuppressors or chemotherapy drugs