A novel design for a velocity-map imaging (VMI) spectrometer with high resolution over a wide energy range surpassing a standard VMI design is reported. The main difference to a standard three-electrode VMI is the spatial extension of the applied field using 11 electrodes forming a thick-lens. This permits measurements of charged particles with higher energies while achieving excellent resolving power over a wide range of energies. Using SIMION simulations, the thick-lens VMI is compared to a standard design for up to 360 eV electrons. The simulations also show that the new spectrometer design is suited for charged-particle detection with up to 1 keV using a repeller-electrode voltage of -30 kV. The experimental performance is tested by laser-induced ionization of rare gases producing electrons up to about 70 eV. The thick-lens VMI is useful for a wide variety of studies on atoms, molecules and nanoparticles in intense laser fields and high-photon-energy fields from high-harmonic-generation or free-electron lasers.