The KCC-Jacobi method has been used for analyzing Garner cancerous model. The KCC theory is based on the assumption that the second-order dynamical system and geodesics equation, in associated Finsler space, are topologically equivalent. The stability (Jacobi stability) based on KCC theory and linear stability of the model are discussed in detail. Further, the effect of parameters on stability and presence of chaos in the model are investigated. The asymptotic behavior of stabilities of model are investigated. This investigation will be helpful in cancer therapy. The numerical examples of particular interest have been taken to compare Jacobi and linear stability and it has been found that Jacobi stability on the basis of KCC theory is global than the linear stability.