Solid organ transplant recipients (OTRs) have an increased cancer risk but their survival once diagnosed with cancer has seldom been assessed. We therefore investigated cancer‐specific survival among OTRs with a wide range of cancer forms nationally in Sweden. The study included 2,143 OTRs with cancer, and 946,089 nontransplanted cancer patients diagnosed 1992–2013. Hazard ratios (HR) and 95% confidence intervals (CI) were estimated using Cox regression models adjusted for age, sex and calendar year. Median follow‐up was 3.1 (range 0–22) years. Overall, OTRs diagnosed with any cancer had a 35% higher rate of cancer death compared to nontransplanted cancer patients (HR: 1.35, 95% CI: 1.24–1.47). Specifically, higher rates of cancer‐specific death were observed among OTRs diagnosed with Hodgkin lymphoma (HR: 15.0, 95% CI: 5.56–40.6), high‐grade non‐Hodgkin lymphoma (HR: 2.68, 95% CI: 1.90–3.77), malignant melanoma (HR: 2.80, 95% CI: 1.74–4.52) and urothelial (HR: 2.56, 95% CI: 1.65–3.97), breast (HR: 2.12, 95% CI: 1.38–3.25), head/neck (HR: 1.55, 95% CI: 1.02–2.36) and colorectal (HR: 1.42, 95% CI: 1.07–1.88) cancer. The worse outcomes were not explained by differences in distribution of cancer stage or histologic subtypes. For other common cancer forms such as prostate, lung and kidney cancer, the prognosis was similar to that in nontransplanted cancer patients. In conclusion, several but not all types of posttransplantation cancer diagnoses are associated with worse outcomes than in the general population. Reasons for this should be further explored to optimize posttransplantation cancer management.