Conventional multi-source waveform inversion using an objective function based on the least-square misfit cannot be applied to marine streamer acquisition data because of inconsistent acquisition geometries between observed and modelled data. To apply the multi-source waveform inversion to marine streamer data, we use the global correlation between observed and modelled data as an alternative objective function. The new residual seismogram derived from the global correlation norm attenuates modelled data not supported by the configuration of observed data and thus, can be applied to multi-source waveform inversion of marine streamer data. We also show that the global correlation norm is theoretically the same as the least-square norm of the normalized wavefield. To efficiently calculate the gradient, our method employs a back-propagation algorithm similar to reverse-time migration based on the adjoint-state of the wave equation. In numerical examples, the multi-source waveform inversion using the global correlation norm results in better inversion results for marine streamer acquisition data than the conventional approach.