Using thin stripe excitation of a 10 ns pulsed laser, we observed robust and bright random laser (RL) emission in high concentrated solutions of poly[2-methoxy-5-(2-ethylhexyloxy)-1,4-phenylenevinylene] (MEH-PPV) and poly[2,6-(4,4-bis-(2-ethylhexyl)-4H-cyclopenta[2,1-b;3,4-b']-dithiophene)-alt-4,7-(2,1,3-benzothiadiazole)] (PCPDTBT). In particular, within the proper excitation intensity range, single line RL emission is observed in both solutions, with full width at half-maximum of 0.17 nm and 0.4 nm for MEH-PPV and PCPDTBT, respectively. The reason for the random laser is that the refractive index fluctuation due to the aggregation in concentrated solution results in spatially extended random lasing modes, which are amplified through traveling light along the interface between solution and cuvette. Our work provides a simple but effective method to achieve bright single-mode RLs, with conversion efficiency on the order of 10%.