A computer program has been developed by the present authors for the curved crack path prediction. We consider the proportional loading condition, and the loading parameter is increased or decreased in such a manner that the brittle crack is quasi-statically growing along the curved trajectory. Although dynamic behavior including inertia effects and dynamic material properties is beyond the scope of the present prediction, we expect that some of the essential features of the curved crack paths observed in actual brittle fracture or fatigue crack propagation can be obtained by the method. The computational prediction is performed by the step-by-step method in cooperation with the stress analysis ahead of the crack tip and the determination of the curved increment of the crack growth. The stress distribution around the crack tip is first calculated by the method of the superposition of analytical and finite-element solutions proposed by Yamamoto et al., where the finite element data generation due to the crack growth process is to a certain extent carried out by automatical mesh rearrangement and nodal renumbering. Then a highly accurate asymptotic representation of the curved crack path, which is introduced in our first report assuming the locally symmetric deformation ahead of the crack tip, is employed for the path prediction. Numerical examples are given for the crack path prediction in DCB type specimen, which was numerically and experimentally investigated in our previous report from the view point of crack path stability. After few steps of numerical calculation unstable crack curving is obtained, and the predicted paths show extremely good agreements with the experimentally measured crack paths. It is also observed that the Mode II stress intensity factor K _II is actually very small during the entire curved crack growth. Application of the present prediction method to more complicated problems, i. e. crack curving in structural elements, the growth of interacting cracks and etc, will be made in subsequent works.