Here's a link to the same basic block. Just leave the sides plain.
Signature Block (quilterscache.com)
One difference, the strip in your pic is narrower than in this pattern. But this at least gives you the idea.
It'd be easier to do it as blocks, with the strip on each, than to do as QSTs with sashing strips, as
Tartan has suggested. IMHO. Then just do your layout to get the pattern.
A very effective and pleasing quilt. The simplicity of it, speaks volumes.