PACS 74.20.-z -Theories and models of superconducting state PACS 74.81.-g -Inhomogeneous superconductors and superconducting systems, including electronic inhomogeneities PACS 73.22.Pr -Electronic structure of graphene Abstract -We propose a new type of non-uniform condensate state in the presence of timereversal symmetry. The underlying platform of this state is a corrugated honeycomb lattice which exhibits an inhomogeneous pseudo magnetic field. Using self-consistent tight binding Bogoliubovde Gennes formalism, we show that an s-wave pairing of chiral carriers in the presence of an inhomogeneous pseudo magnetic field results in a spatially modulated order parameter with the half wavelength of the corrugation. The manner of modulation depends on the fundamental directions of honeycomb lattice, the zigzag and armchair directions. The stability of this inhomogeneous superconductivity is also analyzed and possible experimental realization is discussed.Introduction.-Inhomogeneous superconductivity (IS) with a spatially modulated order parameter has attracted a great deal of attention from both the theoretical [1] and experimental [2-5] points of view. The IS can emerge through a non-trivial pairing between electronic states. The first type of IS was considered by Fulde and Ferrell [6], and Larkin and Ovchinnikov [7] (FFLO). In the FFLO state, the Cooper pairs can be formed through coupling between the imbalanced opposite spin states near the Fermi surface with non zero center-of-mass momentum, resulting in an oscillatory behavior of pairing potential in the real space. The other types of IS are gapped [8][9][10][11] and gapless [12,13] topological FFLO states which are protected against disorders. In contrast to the above mentioned ISs which are made by the magnetic ingredient, the possibility of IS in the absence of magnetic field is indeed an intriguing issue. So the interesting question arises, how is it possible to obtain IS in the presence of time-reversal symmetry?