Pair density wave (PDW) is an exotic state of matter featuring a spatially modulated gap induced by superconducting pairs with nonzero center-of-mass momentum in equilibrium, predicted initially by Fulde, Ferrel, Larkin and Ovchinnikov (FFLO). Experimental evidence demonstrate that such state exists in high magnetic field and breaks the translational symmetry of the lattice. However, to our knowledge, the existence of PDW states in the absence of external magnetic field has not been reported. Utilizing scanning tunneling microscope/microscopy (STM/S), we study such zero-field PDW state in a magnetic iron-based superconductor — EuRbFe₄As₄ (ER1144), which has coexisting helical magnetism (T_m ~15K) and superconductivity (T_c ~ 37K). In this material, at low temperature, we observed a long range, unidirectional, modulated superconducting gap with an incommensurate period of ~8 unit cells. Both our STM/S results and other bulk measurements show the absence of charge or spin density waves, indicating that the PDW state in ER1144 is a primary, zero-field superconducting instability, in contrast to previous PDW measurements in cuprates, Kagome materials and charge density wave materials. Interestingly, we found that the PDW state is absent inside the vortex core upon applying external magnetic field. When the temperature rises above the T_m, the spatial modulations are completely suppressed but only a uniform superconducting gap survives. And both four-fold rotational symmetry and translational symmetry recover, indicating that the PDW is a smectic order.