This paper deals with the following Cauchy problem for critical heat equation with drift term {u(t)= triangle u+del lna(x)del u+|u|4/n-2u,for (x,t)is an element of R(n)x(0,+infinity), u(,0) =u(0), for x is an element of R-n, where a(x) is a positive smooth bounded function in R-n,n >= 6. Assume that the eigenvalues of matrix A(q), denoted as sigma(i), i= 1,,n, satisfy sigma i+infinity, here 0< mu(j)(t)-> 0 exponentially as t ->+infinity.
