We carried out the energy scan between E(CM) = 58 and 60 GeV. at the TRISTAN e+ e- collider to search for the possible narrow resonance suggested by the L3 experiment at LEP. The total cross sections are measured for gammagamma, multihadron, e+ e- and mu+ mu- productions at ten energy points covering this energy range almost uniformly. The results are in good agreement with the Standard Model predictions, and 95% confidence level upper limits are set to GAMMA(ee) x BR of the hypothetical scalar and tensor resonances.