Submitted on 21 Apr 2008 (v1), last revised 24 Apr 2008 (this version, v2).-- 13 pages, 4 figures.-- v2: reference added.We study non-perturbative moduli superpotentials with positive exponents, i.e. the form like Ae^{aT} with a positive constant a and the modulus T. These effects can be generated, e.g., by D-branes which have negative RR charge of lower dimensional D-brane. The scalar potentials including such terms have a quite rich structure. There are several local minima with different potential energies and a high barrier, whose height is of O(M_p^4). We discuss their implications from the viewpoints of cosmology and particle phenomenology, e.g. the realization of inflation models, avoiding the overshooting problem. This type of potentials would be useful to realize the inflation and low-energy supersymmetry breaking.H. A., T. H. and T. K. are supported in part by the Grant-in-Aid for Scientific Research No. 182496, No. 194494 and No. 20540266 from the Ministry of Education, Culture, Sports, Science and Technology of Japan. O. S. is supported by the MEC project FPA 2004-02015 and the Comunidad de Madrid project HEPHACOS (No. P-ESP-00346).Peer reviewed