For both plant (e.g. potato) and animal (e.g. salmon) species, unveiling the genetic architecture of complex traits is key to the genetic improvement of polyploids in agriculture. F1 progenies of a biparental cross are often used for quantitative trait loci (QTL) mapping in outcrossing polyploids, where haplotype reconstruction by identifying the parental origins of marker alleles is necessary. In this work, we build a novel and integrated statistical framework for multilocus haplotype reconstruction in a full-sib tetraploid family from biallelic marker dosage data collected from single nucleotide polymorphism (SNP) arrays or next-generation sequencing technology, given a genetic linkage map. Compared to diploids, in tetraploids additional complexity needs to be addressed including double reduction and possible preferential pairing of chromosomes. We divide haplotype reconstruction into two stages: parental linkage phasing for reconstructing the most probable parental haplotypes, and ancestral inference for probabilistically reconstructing the offspring haplotypes conditional on the reconstructed parental haplotypes. The simulation studies and the application to real data from potato show that the parental linkage phasing is robust to complex chromosome pairing behaviors during meiosis, to various marker segregation types, to erroneous genetic maps except for long-range disturbances of marker ordering, to various amounts of offspring dosage errors (up to ∼ 20%), and to various fractions of missing data in parents and offspring dosages, and that the subsequent ancestral inference is accurate.