Motivated by recent inelastic neutron scattering experiments up to a high-energy region forLa-based cuprates, we compute (q, ω) maps of the imaginary part of the dynamical magnetic susceptibility χ(q, ω) in the slave-boson mean-field approximation to the two-dimensional t-J model.While the strong spectral weight appears at incommensurate positions, namely at q = Q ≡ (π, π), for low energy, the incommensurate signals disperse with increasing ω and finally merge into a commensurate signal at a particular energy ω = ω Q . These features are seen in both the d-wave pairing state and the normal state. In particular, the incommensurate signals below ω Q in the normal state are due to the Fermi surface geometry, which we expect for La-based cuprates because of a tendency to d-wave type Fermi surface deformations. Above ω Q , strong signals appear to trace an upward dispersion especially for a low doping rate in the d-wave pairing state while typically broad spectral weight is obtained around q = Q in the normal state. Salient features of magnetic excitations in La-based cuprates are thus naturally captured in terms of particle-hole excitations. Global understanding of magnetic excitations in high-T c cuprates is discussed through a comparison with magnetic excitations in YBa 2 Cu 3 O y .