Abstract Background The knowledge of the key factors associated with fertility desire among people living with HIV/AIDS is crucial for the efficient planning of maternal and child health care programs. Fertility desire has generally increased among women of reproductive age in Rwanda. However, its level and determinants among women living with HIV/AIDS (WLHA) are currently not well known in the context of Rwanda. The present study aimed to fill in this knowledge gap. Methods Data were extracted from the 2015 Rwanda demographic and health survey (RDHS) for 243 HIV-positive women of reproductive age. Univariate and multivariable logistic regression analyses were conducted in order to identify the most influential factors. Results The prevalence of desire to have another child in HIV-positive women was found to be as high as 40.7%. Multivariable logistic regression analyses showed that the woman’s age of 35–49 years (AOR = 0.051, 95% CI: 0.013–0.204), woman’s parity of 3 children or above (AOR = 0.177, 95% CI: 0.037–0.837), being employed (AOR = 0.298, 95% CI: 0.113–0.782) and currently using contraceptives (AOR = 0.146; 95% CI: 0.057–0.375) were significantly associated with low odds of fertility desire among HIV- positive women in Rwanda. Women younger than 25 years, with no living child, or who were unemployed or who were not using any contraceptive were significantly associated with greater odds of desire to have another child than did other HIV- positive women. A woman whose partner's desire for children is different from hers was associated with about four times higher odds (AOR = 3.752; 95% CI: 1.203–11.702) of desire for more children than women who desire the same as their partners. Conclusion Fertility desire in WLHA is currently high in Rwanda. It is significantly influenced by demographic and socioeconomic factors. The Rwanda’s health care system should be prepared to intensify the required services for the prevention of the vertical transmission of HIV, the delivery of maternal and child health care services, and the support to WLHA in planning their fertility. Interventions should target low-parity young women, with a particular focus on meeting their contraceptive needs.