A sequential pump-dump control scenario for photoisomerization competing with direct photodissociation of a chiral molecule is derived by using a global optimization method. As an example, H2POSD with axial chirality is considered. The first excited electronic state with n-sigma* electronic configuration is characterized by a repulsive potential that leads to P-S bond breaking. In this scenario, a first pump-dump sequence creates a nuclear wave packet having enough kinetic energy to cross the potential barrier in the ground state. This wave packet moves from one potential well corresponding to one of the optical isomers to the other in the electronic ground state. This transfer minimizes effects of the competing photodissociation. The second pump-dump sequence converts the wave packet into one having a small amount of kinetic energy via excitation to the first excited state. A stimulated Raman adiabatic passage (STIRAP) is applied to the same system for comparison. The yield of the photoisomerization obtained by using the STIRAP method is less than 0.1%, while that of using the sequential pump-dump pulse method is about 25%.