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Low-frequency electronic noise is an important parameter used for the electronic and sensing applications of transistors. Here, we performed a systematic study on the low-frequency noise mechanism for both p-channel and n-channel MoTe2 field-effect transistors (FET) at different temperatures, finding that low-frequency noise for both p-type and n-type conduction in MoTe2 devices come from the variable range hopping (VRH) transport process where carrier number fluctuations (CNF) occur. This process results in the broad distribution of the waiting time of the carriers between successive hops, causing the noise to increase as the temperature decreases. Moreover, we found the noise magnitude for p-type MoTe2 FET hardly changed after exposure to the ambient conditions, whereas for n-FET, the magnitude increased by nearly one order. These noise characteristics may provide useful guidelines for developing high-performance electronics based on the emerging transition metal dichalcogenides.