The ground state properties of a frustrated spin-1/2 system is studied on a trellis ladder which is composed of two zigzag ladders interacting through rung interactions. The presence of rung interaction between the zigzag ladders induces a non-magnetic ground state, although, each of zigzag ladders has ferromagnetic order in weak anti-ferromagnetic leg interaction limit. The rung interaction also generates rung dimers and opens spin gap which increases rapidly with rung interaction strength. The correlation between spins decreases exponentially with the distance between them. Figure 1: Two coupled zigzag ladders form trellis ladder. The broken lines show the extension of trellis ladder to trellis lattice structure. The arrows show respective spin arrangements. The reference site is labeled by '0' and the distances of all other sites are shown with respect to it. The distance of the sites in the same zigzag ladder as the reference site are written in bold numbers, and the sites on the other ladder are written in normal numbers.and rung couplings of a normal ladder, respectively and J 1 is inter-ladder coupling through zigzag bonds.There are several theoretical studies for two coupled zigzag ladders, e.g. a two-leg honeycomb ladder is considered in Ref. [19], where both J 1 and J 2 are AFM, but J 3 can be either FM or AFM. This system shows two types of Haldane phases for the FM J 3 and, columnar dimer and rung singlet phases for the AFM J 3 . Normand et al. considered the similar coupled ladders with all three AFM J 1 , J 2 and J 3 interactions. They find dimerized chains for large J 2 and small J 3 limit, spiral long range order for both large J 2 and J 3 limit, Néel long range order in the small J 2 < 0.4 and for all J 3 [20]. Ronald et al. have shown the effect of inter-chain coupling on spiral ground state of J 1 − J 2 model [21]. The effect of inter-ladder coupling on spin gap and magnon dispersion has been discussed in [22] exploiting a theoretical model which has also been