Let $\GG(k,n)$ be the Grassmannian of $k$-subspaces in an $n$-dimensional complex vector space, $k \ge 3$. Given a projective variety $X$, its $s$-secant variety $\sigma_s(X)$ is defined to be the closure of the union of linear spans of all the $s$-tuples of independent points lying on $X$. We classify all defective $\sigma_s(\GG(k,n))$ for $s \le 12$.}
