Ocean waves provide a promising and abundant renewable energy resource. One reason wave energy technology is still not mature enough for commercialization is the high unit cost of generated electricity. This needs to be improved by a combination of device and associated controller design. A multi-float and multi-mode-motion wave energy converter (M-WEC) enables much higher energy conversion compared with a single-float, single-mode WEC (S-WEC); however, the added complexity in dynamics of a M-WEC makes the corresponding controller design more challenging. While the majority of current WEC control research has been based on the control of S-WECs it has shown that control can significantly improve energy conversion. This paper aims to design a linear non-causal optimal controller for a M-WEC to demonstrate that this improvement also applies to more complex WEC systems. We choose a multi-body attenuator type M-WEC called M4 as a case study for which the desirable feature of predominantly linear dynamics has been demonstrated. This means that a linear controller can be designed based on a linear hydrodynamic model without introducing an intractable computational burden for real-time controller implementation. Numerical results show that the linear non-causal optimal controller can significantly improve the power capture of M4 over a broad range of peak spectral wave periods by $\text{40}{\%}$ to $\text{100}{\%}$ .