Abstract: For We study the Feigin-Odesskii Poisson structures on a complex projective spaces. These are given by a normal elliptic curve E inside CP^n and a vector field on E. For a Feigin-Odesskii Poisson structure, the symplectic leaves of dim 2k foliate the (non-singular part of the) k-th secant variety of E. For the CP^2 case, we present an approach to characterize the Poisson structure via defining a natural co-Higgs bundle on CP^1=E/involution. This should shed the light on the structure of so called bosonic coordinates on the symplectic leaves, which was our original motivation. For the higher dimensional case, we can apply our technique to describe the Poisson structure on the first secant variety of E. We hope to generalize the results to the higher secant varieties in the future.