This paper studies the crack propagation path in a ceramic/metal functionally graded material plate (FGP) with two end cracks under a transient temperature field. When the FGP is subjected to severe thermal conditions, a single crack or multiple cracks often occur on the ceramic surface at cooling process. The crack may propagate along thickness direction or parallel direction to the surface. The crack propagation paths are influenced by heating temperature, a compositional profile of the FGP, interaction among multiple cracks, and so on. The crack propagation path is calculated as a linear quasi-static thermoelastic problem for a plane strain state by use of a finite element method. The crack paths are roughly classified into two cases; one is straight propagation path and other is curved path. These phenomena are discussed for two-cracks propagation.