The practical application of quasicrystals (QCs) as thermoelectric materials makes icosahedral (i-) Al–Pd–Re QC attractive because of its moderate electrical conductivity (~280 Ω−1 cm−1), relatively high Seebeck coefficient (~100 μV K−1), and low thermal conductivity (~1.3 W m−1 K−1) at room temperature. To develop a thermoelectric Π-shaped power generation module, we need both p- and n-type thermoelectric materials. In this work, we aimed to develop an n-type i-Al–Pd–Re-based QC and investigated the effect of Co substitution for Re on the thermoelectric properties, i.e., the electron-doping effect. We synthesized dense bulk samples with nominal compositions of Al71Pd20(Re1−xCox)9 (x = 0, 0.1, 0.2, 0.3, 0.4, 0.5) via arc-melting, annealing, and sintering methods. We found that Co can produce n-type carriers in dilute substitution amounts of x = 0.1 and 0.2; however, the Seebeck coefficient at 300 K showed an n- to p-type transition with increasing x. This indicates that a simple rigid-band approximation is not applicable for i-Al–Pd–Re QC, which makes it difficult to synthesize an n-type i-Al–Pd–Re-based QC. Although the thermal conductivity was reduced from 1.28 (x = 0) to 1.08 W m−1 K−1 (x = 0.3) at 373 K by lowering of the electron thermal conductivity (electrical conductivity) and the alloying effect via Co substitution, the dimensionless figure of merit was not enhanced because of lowering of the power factor for all samples. The elastic moduli of i-Al–Pd–Re QC decreased by Co substitution, indicating that i-Al–Pd–Re-Co QC had a more ionic and brittle character.