African swine fever virus (ASFV) has become widespread in Europe, Asia and elsewhere, thereby causing extensive economic losses. The viral genome includes nearly 200 genes, but their expression within infected pigs has not been well characterized previously. In this study, four pigs were infected with a genotype II strain (ASFV POL/2015/Podlaskie); blood samples were collected before inoculation and at both 3 and 6 days later. During this period, a range of clinical signs of infection became apparent in the pigs. From the blood, peripheral blood mononuclear cells (PBMCs) were isolated. The transcription of the ASFV genes was determined using RNAseq on poly(A)+ mRNAs isolated from these cells. Only very low levels of virus transcription were detected in the PBMCs at 3 days post-inoculation (dpi) but, at 6 dpi, extensive transcription was apparent. This was co-incident with a large increase in the level of ASFV DNA within these cells. The pattern of the virus gene expression was very reproducible between the individual pigs. Many highly expressed genes have undefined roles. Surprisingly, some genes with key roles in virus replication were expressed at only low levels. As the functions of individual genes are identified, information about their expression becomes important for understanding their contribution to virus biology.