By using complex variable method, the frictionless contact problem in one-dimensional orthorhombic quasicrystals was discussed in the paper .On the contact surface, the explicit expressions of stress functions, contact stress and contact displacement were obtained under action of a rigid flat punch. The results showed that :(1)contact stress exhibits the singularities in the edge of the contact zone; (2)The contact displacement is proportion to the applied force. Numerical examples were used to analysis and verify the correctness of the results. In special cases, the conclusions can reduce to the solutions of the frictionless contact problem in one-dimensional Tetragonal and hexagonal quasicrystals. The obtainable results provide the important mechanics parameter for contact deformation of the quasicrystal.