We present a Herschel/Spectral and Photometric Imaging Receiver (SPIRE) survey of three protoclusters at z=2-3 (2QZCluster, HS1700, SSA22). Based on the SPIRE colours (S_350_/S_250_ and S_500_/S_350_) of 250{mu}m sources, we selected high-redshift dusty star-forming galaxies potentially associated with the protoclusters. In the 2QZCluster field, we found a 4{sigma} overdensity of six SPIRE sources around 4.5-arcmin (~2.2Mpc) from a density peak of H {alpha} emitters at z=2.2. In the HS1700 field, we found a 5{sigma} overdensity of eight SPIRE sources around 2.1-arcmin (~1.0Mpc) from a density peak of Lyman-break galaxies at z=2.3. We did not find any significant overdensities in SSA22 field, but we found three 500 {mu}m sources are concentrated 3-arcmin (~1.4Mpc) east to the Ly {alpha} emitters overdensity. If all the SPIRE sources in these three overdensities are associated with protoclusters, the inferred star formation rate densities are 10^3^-10^4^ times higher than the average value at the same redshifts. This suggests that dusty star formation activity could be very strongly enhanced in z~2-3 protoclusters. Further observations are needed to confirm the redshifts of the SPIRE sources and to investigate what processes enhance the dusty star formation activity in z~2-3 protoclusters.