The quasi-periodic structures of Fibonacci sequence composed of conventional materials were proposed, and their spatial transmittance properties were investigated by using the transfer matrix method. The corresponding low-pass spatial filters with a small angle-domain bandwidth were designed based on these good spatial transmittance properties. The numerical simulation results show that, the angle-domain bandwidth can be tuned by changing the structure types and sequence numbers, and the angle-domain bandwidth of the filters becomes smaller and smaller with the increase of the sequence number or m value of Fibonacci sequence F(m,1). On the basis of the above regulation, the accurate adjustment can be made by changing the refractive-index parameter of the quasi-periodic structures. Compared to the former Metamaterial spatial filters with a small angle-domain bandwidth, the spatial filters based on Fibonacci quasi-periodic structures are more simple to be made and more likely to be applied to a new generation of high-power laser system.