  We perform a systematic investigation on the ground state of an asymmetric
two-leg spin ladder (where exchange couplings of the legs are unequal) with
ferromagnetic (FM) nearest-neighbor interaction and diagonal anti-ferromagnetic
frustration using the Density Matrix Renormalization Group (DMRG) method. When
the ladder is strongly asymmetric with moderate frustration, a magnetic canted
state is observed between a FM state and a singlet dimerized state. The phase
boundaries are dependent on the asymmetric strength $\alpha_{a}$. On the other
hand, when the asymmetric strength is intermediate, a so-called spin-stripe
state (spins align parallel on same legs, but antiparallel on rungs) is
discovered, and the system experiences a first-order phase transition from the
FM state to the spin-stripe state upon increasing frustration. We present
numerical evidence to interpret the phase diagram in terms of frustration and
the asymmetric strength.
