  We propose a sufficient criterion
${S}=\lambda_1+\lambda_2-(\lambda_1-\lambda_2)^2<0$ to detect
Einstein-Podolsky-Rosen steering for arbitrary two-qubit density matrix
$\rho_{AB}$. Here $\lambda_1,\lambda_2$ are respectively the minimal and the
second minimal eigenvalues of $\rho^{T_B}_{AB}$, which is the partial transpose
of $\rho_{AB}$. By investigating several typical two-qubit states such as the
isotropic state, Bell-diagonal state, maximally entangled mixed state, etc., we
show this criterion works efficiently and can make reasonable predictions for
steerability. We also present a mixed state of which steerability always
exists, and compare the result with the violation of steering inequalities.
