We consider $ϵ$-approximation schemes for concave quadratic programming. Because the existing definition of $ϵ$-approximation for combinatorial optimization problems is inappropriate for nonlinear optimization, we propose a new definition for $ϵ$-approximation. We argue that such an approximation can be found in polynomial time for fixed $ϵ$ and $k$, where $k$ denotes the number of negative eigenvalues. Our algorithm is polynomial in 1/$ϵ$ for fixed $k$, and superexponential in $k$ for fixed $ϵ$.