This article is concerned with the initial-value problem of a Schrödinger-Hartree equation in the presence of anisotropic partial/whole harmonic confinement. Firstly, we get a sharp threshold for global existence and finite time blow-up at the ground state mass in the L 2 -critical case. Then, some new cross-invariant manifolds and variational problems are constructed to study blow-up versus global well-posedness criteria in the L 2 -critical and L 2 -supercritical cases. Finally, we research the mass concentration phenomenon of blow-up solutions and the dynamics of the L 2 -minimal blow-up solutions in the L 2 -critical case. The main ingredients of the proofs are the variational characterization of the ground state, a suitable refined compactness lemma and scaling techniques. Our conclusions extend and compensate for some previous results.