ABSTRACT In this article, we estimate the eccentricity of 10 binary black holes (BBHs) in the Gravitational-Wave Transient Catalog GWTC-1 by using the inspiral-only BBH waveform template EccentricFD. First, we test our method with simulated eccentric BBHs. Afterwards we apply the method to real BBH gravitational-wave data. We find that the BBHs in GWTC-1, with the exception of GW151226, GW170608 and GW170729, show very small eccentricity. Their upper limits on eccentricity range from 0.033–0.084 with 90 per cent credible interval at a reference frequency of 10 Hz. For GW151226, GW170608 and GW170729, the upper limits are higher than 0.1. The relatively large eccentricity of GW151226 and GW170729 is probably due to ignoring χeff and the low signal-to-noise ratio, and GW170608 is worthy of follow-up research. We also point out the limitations of the inspiral-only non-spinning waveform template in eccentricity measurement. Measurement of BBH eccentricity helps us to understand its formation mechanism. With an increase in the number of BBH gravitational-wave events and a more complete eccentric BBH waveform template, this will become a viable method in the near future.