Abstract We describe the T-ideal of identities and the T-space of central polynomials for the unitary finite dimensional Grassmann algebra over a finite field. Key Words: Central polynomialsFinite fieldGrassmann algebraIdentitiesT-idealT-spaceUnitary2000 Mathematics Subject Classification: Primary 16R10Secondary 16R4016S1015A75 Notes Communicated by V. A. Artamonov.