Synaptic plasticity is vital for learning and memory in the brain. It consists of long-term potentiation (LTP) and long-term depression (LTD). Spike frequency is one of the major components of synaptic plasticity in the brain, a noisy environment. Recently, we mathematically analysed the frequency-dependent synaptic plasticity (FDP) in vivo and found that LTP is more likely to occur with an increase in the frequency of background synaptic activity. Previous studies suggest fluctuation in the amplitude of background synaptic activity. However, little is understood about the relationship between synaptic plasticity and the fluctuation in the background synaptic activity. To address this issue, we performed numerical simulations of a calcium-based synapse model. Then, we found attenuation of the tendency to become LTD due to an increase in the fluctuation of background synaptic activity, leading to an enhancement of synaptic weight. Our result suggests that the fluctuation affect synaptic plasticity in the brain.