Sex allocation theory predicts that parents should adjust their investment between female and male offspring when the fitness return of producing them differs. Genome-wide heterozygosity is related to many aspects of individual fitness, and an individual’s heterozygosity is usually determined by the genetic characteristics of its parents. When heterozygosity affects fitness differently for female and male offspring, parents may be expected to manipulate offspring sex ratio based on their own genetic characteristics. We examined whether parental genetic characteristics affected primary offspring sex ratios in a small passerine bird, the black-throated tit (Aegithalos concinnus). We found that offspring heterozygosity was significantly related to the heterozygosity of parents and the relatedness between parents. Importantly, genetic heterozygosity had a significantly negative effect on the survival of male but not female black-throated tits, implying higher variance in fitness in males than in females regarding the genetic heterozygosity inherited from parents. This sex-specific effect of heterozygosity on fitness provides black-throated tit parents with a potential reason to adjust offspring sex ratio in relation to their own genetic characteristics. However, although we found a seasonal decline of offspring sex ratio (proportion of males), offspring sex ratio was associated with neither the relatedness between parents nor the heterozygosity of parents. The results suggest that at least based on current data, there is a lack of evidence that black-throated tit parents manipulate offspring sex ratio with respect to their own genetic characteristics. The correlation between genome-wide heterozygosity and individual fitness has been extensively studied, but its potential role in mediating parental manipulation of offspring sex ratio has received attention only recently. If heterozygosity affects fitness differently for the two sexes of offspring, parents are likely to adjust their investment between female and male offspring based on their own genetic characteristics. This is because their own genetic characteristics determine their offspring’s heterozygosity and therefore fitness returns to parents. Existing studies have provided support to this hypothesized manipulation of offspring ratio, but studies in the area remain scarce. Our study shows that parents of a bird species do not manipulate offspring sex ratio with respect to their own genetic characteristics, even when there is a sex-specific heterozygosity-fitness correlation.