Reconstruction of family trees, or pedigree reconstruction, for a group of individuals is a fundamental problem in genetics. The problem is known to be NP-hard even for datasets known to only contain siblings. Some recent methods have been developed to accurately and efficiently reconstruct pedigrees. These methods, however, still consider relatively simple pedigrees, for example, they are not able to handle half-sibling situations where a pair of individuals only share one parent. In this work, we propose an efficient method, IPED2, based on our previous work, which specifically targets reconstruction of complicated pedigrees that include half-siblings. We note that the presence of half-siblings makes the reconstruction problem significantly more challenging which is why previous methods exclude the possibility of half-siblings. We proposed a novel model as well as an efficient graph algorithm and experiments show that our algorithm achieves relatively accurate reconstruction. To our knowledge, this is the first method that is able to handle pedigree reconstruction based on genotype data only when half-sibling exists in any generation of the pedigree.