Trapping particles (atoms or molecules) allows long interaction time and therefore potentially high resolution in precision measurements. Moreover, the particles in the trap are thermally isolated from the outside world and can be cooled to very low temperatures. As a result, the atomic (or molecular) traps have been widely used in many research areas. However, the molecules in these traps exhibiting zero field in the trap center undergo nonadiabatic transitions, which is the major loss of particles. The loss of atoms in this type of trap seriously hinders the generation of the first BEC (Bose-Einstein condensates). In this paper, we propose a chip-based controllable Ioffe-type electrostatic mirotrap, in which nonadabatic loss can be avoided due to the non-zero electric field. The mirotrap is composed of a pair of L-typed gold wires, which is 1 m in height and deposited on a glass substrate. The non-zero potential well originated in the microsize electrodes offers a steep gradient enable to trap low-field-seeking state polar molecules. The electric field strength in the trap center can be changed in a wide range by adjusting the applied voltage or/and the widths of the electrodes. For instance, under the conditions in the paper, the electric field strength in the trap center can be changed from 0.15 to 5.5 kV/cm. The height of the potential well is about 10 m above the chip and can also be tuned in a large range by adjusting the parameters of the electrodes. Under the conditions in the paper, the height of the potential well can be adjusted from 6.0 to 17.0 m. The electric fields of the microtrap near the surface of the chip are calculated by using a finite element software. Monte-Carlo simulations of the loading and the trapping processes are also carried out in order to justify the feasibility of our scheme. Taking ND3 molecules for example, the loading efficiency of molecules as a function of longitudinal velocity of molecular packet is studied. Our proposed surface microtrap can be used not only for integrating the molecular chips but also for producing the quantum degenerate gas near the chip surface. It offers a platform for many research fields such as precision measurements, quantum computing, surface cold collisions and cold chemistry.