Micro-structured targets have been widely used in the interaction between ultra-intense laser and target, aiming at improving the electron accelerating efficiency. In this paper, we perform two-dimensional particle-in-cell (PIC) simulations to study the interaction of the ultra-intense laser pulse with the micro-structured foam-attached target (the foam is composed of low density bubbles and high density interfaces between the bubbles). It is found that at the beginning of the laser-plasma interaction, the fast electrons accelerated at the front surface of the foam freely propagate into the target and drive a return current of cold background electrons. These cold background electrons are restricted to propagate along the interfaces between the bubbles in the foam due to the self-generated large sheath field. As a result, small current filaments are generated in the foam, which then leads to the generation of randomly distributed megagauss magnetic field in the foam layer. This quasistatic magnetic field then acts as an energy-selective " magnetic barrier”: the low-energy electrons are reflected back into the laser acceleration region while the high-energy electrons can penetrate through it. If the reflected electrons enter into the laser field with proper phases, they can be further accelerated to higher energy through cooperative actions of the ultra-intense laser pulse and the sheath field generated due to plasma expansion at the target surface. Our simulation results show that many of the laser accelerated low-energy electrons can be reflected back and accelerated several times until they gain enough energy to penetrate through the magnetic barrier. This is termed the " multiple acceleration mechanism”. Due to this mechanism, the electron acceleration efficiency in the foam-coated target with a thickness of several microns is significantly enhanced in comparison with that in the plane target. This enhancement in the electron acceleration efficiency will be beneficial to many important applications such as the fast ignition. Additionally, foam-coated targets with different bubble radii and layer thickness are also studied, and it is found that the yield of the high energy electrons increases with the radius of bubble size more efficiently than with the bubble thickness. In order to understand the physics more clearly, a single particle model is developed to analyze the simulation results.