I study the estimation of peer effects with group heterogeneity through social networks when researchers do not observe the entire network structure. The main assumption I set is that the observed partial network data is sufficient to consistently estimate the network formation model that generates the true network data. Examples include sampled networks, censored networks, misclassified links, and aggregated relational data. I propose a pseudo maximum likelihood approach that consistently estimates the peer effect parameter based on the network formation model and the observed network data. I provide an empirical application to the study of peer effects on fast food consumption and show that network data errors have a first-order bias on estimated peer effects.