An olefin resin having requirements (I) to (VI) is provided: (I) a grafted olefin polymer containing a main chain with an ethylene/α-olefin copolymer and a side chain with a propylene polymer; (II) the ratio P wt % of propylene polymer is from 5 to 60 wt %; (III) when the ratio of the amount of a component(s) having a peak temperature of a differential elution curve as measured by CFC using o-dichlorobenzene of less that 65° C., to the amount of (β) taken as E wt %, the value a represented by an equation (Eq-1), is 1.4 or more; (IV) the melting point (Tm) is 120 to 165° C. and the glass transition temperature (Tg) is −80 to −30° C., as measured by DSC; (V) the hot xylene-insoluble content is less than 3 wt %; and, (VI) the limiting viscosity as measured in decalin at 135° C. is 0.5 to 5.0 dl/g.