The Technical Design for the COMET Phase-I experiment is presented in this paper. COMET is an experiment at J-PARC, Japan, which will search for neutrinoless conversion of muons into electrons in the field of an aluminum nucleus ($\mu$–$e$ conversion, $\mu^{-}N \rightarrow e^{-}N$); a lepton flavor-violating process. The experimental sensitivity goal for this process in the Phase-I experiment is $3.1\times10^{-15}$, or 90% upper limit of a branching ratio of $7\times 10^{-15}$, which is a factor of 100 improvement over the existing limit. The expected number of background events is 0.032. To achieve the target sensitivity and background level, the 3.2 kW 8 GeV proton beam from J-PARC will be used. Two types of detectors, CyDet and StrECAL, will be used for detecting the $\mu$–$e$ conversion events, and for measuring the beam-related background events in view of the Phase-II experiment, respectively. Results from simulation on signal and background estimations are also described.