The nature of the pseudogap in high transition temperature (high-Tc) superconducting cuprates has been a major issue in condensed matter physics. It is still unclear whether the high-Tc superconductivity can be universally associated with the pseudogap formation. Here we provide direct evidence of the existence of the pseudogap phase via angle-resolved photoemission spectroscopy in another family of high-Tc superconductor, iron-pnictides. Our results reveal a composition dependent pseudogap formation in the multi-band electronic structure of BaFe2(As1-xPx)2. The pseudogap develops well above the magnetostructural transition for low x, persists above the nonmagnetic superconducting dome for optimal x and is destroyed for x ~ 0.6, thus showing a notable similarity with cuprates. In addition, the pseudogap formation is accompanied by inequivalent energy shifts in xz/yz orbitals of iron atoms, indicative of a peculiar iron orbital ordering which breaks the four-fold rotational symmetry.