We have carried out a deep imaging survey for H \alpha emitting galaxies at z \approx 0.24 using a narrowband filter tuned with the redshifted line . The total sky area covered is 706 arcmin ^ { 2 } within a redshift range from 0.234 to 0.252 ( \delta z =0.018 ) . This corresponds to a volume of 3.9 \times 10 ^ { 3 } Mpc ^ { 3 } when \Omega _ { matter } = 0.3 , \Omega _ { \Lambda } = 0.7 , and H _ { \mathrm { 0 } } =70 km s ^ { -1 } Mpc ^ { -1 } are adopted . We obtain a sample of 348 H \alpha emitting galaxies whose observed emission-line equivalent widths are greater than 12 Å . We find an extinction-corrected H \alpha luminosity density of 10 ^ { 39.65 ^ { +0.08 } _ { -0.12 } } ergs s ^ { -1 } Mpc ^ { -3 } . Using the Kennicutt relation between the H \alpha luminosity and star formation rate , the star formation rate density in the covered volume is estimated as 0.036 ^ { +0.006 } _ { -0.012 } M _ { \sun } yr ^ { -1 } Mpc ^ { -3 } . This value is higher by a factor of 3 than the local SFR density .