Aims. We present the first results of an ongoing project devoted to the search of giant radio halos in galaxy clusters located in the redshift range z =0.2-0.4. One of the main goals of our study is to measure the fraction of massive galaxy clusters in this redshift interval hosting a radio halo, and to constrain the expectations of the particle re-acceleration model for the origin of non-thermal radio emission in galaxy clusters. Methods. We selected 27 REFLEX clusters and here we present Giant Metrewave Radio Telescope (GMRT) observations at 610 MHz for 11 of them. The sensitivity (1\sigma) in our images is in the range 35-100 \muJy beam super(-1) for all clusters. Results. We found three new radio halos, doubling the number of halos known in the selected sample. In particular, giant radio halos were found in A 209 and RXCJ 2003.5-2323, and one halo (of smaller size) was found in RXCJ 1314.4-2515. Candidate extended emission on smaller scale was found around the central galaxy in A 3444 which deserves further investigation. Furthermore, a radio relic was found in A 521, and two relics were found in RXCJ 1314.5-2515. The remaining six clusters observed do not host extended emission of any kind.