Polarization measurement of the background stars in the region of dark globules is important to study the magnetic field geometry and grants characteristics in the globule. These parameters are important for the formation and evolution of dark globules. We made Polarimetric observations of stars in three nearby dark clouds - B5, L134 and Heiles Cloud 2. Polarization measurements of stars in the region of B5 were made with ‘MINIPOL’ (Frecker and Serkowski, 1976) on 61″ telescope of University of Arizona. Observations for the stars in the region of L134 and Heiles Cloud 2 were made using PRL Polarimeter (Deshpande et al. 1985) on 1 meter telescope of Indian Institute of Astrophysics, Bangalore. Results are presented and discussed here. Figure 1 shows the polarization vectors projected on the sky plane for the above globules.