Result Based Financing (RBF) has been implemented in health systems across low and middle-income countries (LMICs), with the objective of improving population health. Most evaluations of RBF schemes have focused on average programme effects for incentivised services. There is limited evidence on the potential effect of RBF on health outcomes, as well as on the heterogeneous effects across socio-economic groups and time periods. This study analyses the effect of Zimbabwe's national RBF scheme on neonatal, infant and under five mortality, using Demographic and Health Survey data from 2005, 2010 and 2015. We use a difference in differences design, which exploits the staggered roll-out of the scheme across 60 districts. We examine average programme effects and perform sub-group analyses to assess differences between socio-economic groups. We find that RBF reduced under-five mortality by two percentage points overall, but that this decrease was only significant for children of mothers with above median wealth (2.7 percentage points) and education (2.1 percentage points). RBF increased institutional delivery by seven percentage points - with a statistically significant effect for poorer socio-economic groups and least educated. We also find that RBF reduced c-section rates by three percentage points. We find no detectable effect of RBF on other incentivised services. When considering programme effects over time, we find that effects were only observed during the second phase of the programme (March 2012) with the exception of c-sections, which only reduced in the longer term. Further research is needed to examine whether these findings can be generalised to other settings.