  Frustrated spin ladders show magnetization plateaux depending on the
rung-exchange interaction and frustration defined by the ratio of first and
second neighbor exchange interactions in each chain. This paper is the first
report on its magnetic phase diagram. Using the variational matrix-product
state method, we accurately determine phase boundaries. Several kinds of
magnetization plateaux are induced by the frustration and the strong
correlation among quasi-particles on a lattice. The appropriate description of
quasi-particles and their relevant interactions are changed by a magnetic
field. We find that the frustration differentiates the triplet quasi-particle
from the singlet one in kinetic energy.
