Based upon the geometrical and topological method, the conformal anomaly for pure gravity in a curved space-time is discussed, and a new expression αεabcdΩabΛΩcd+βεabcdHabΛHcd of the conformal anomaly for pure gravity is obtained, where α, βare two arbitrary constants,Ωab and Hab are Riemann curvature 2-form and eonformal invariant curvature 2-form respectively introduced by Thomas. In the expression the first term is proportional to Euler class, the second term contains not only the ordinary Weyl tensor square but also the other conformal invariants.
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