The coronavirus disease 2019 (COVID-19), which emerged from Wuhan, China, is now a pandemic, affecting across the globe. Bangladesh also is experiencing the rapid growth of COVID-19 infection and death cases started from 8th March 2020. The purpose of providing a simple yet effective explanatory model for prediction of the future evolution of the contagion and verification of the effectiveness of the containment and lockdown measures in Bangladesh. In this study, using a modified SIR (Susceptible-Infected-Recovered) model a forecast is generated to predict the trends of COVID-19 cases in Bangladesh. The epidemic model was proposed to accommodate the effects of lockdown and individual based precautionary measures. Data has been taken and analyzed for before and after the movement control order (MCO) and during the MCO period. Modified SIR model in this work offers us an idea how the outbreak would progress based on the current data. It also has estimated that, the peak in terms of the number of infected cases will start from last of June 2020. For the total population (100%) the model gets the peaks at 214875 (infected cases) and 7743 (death cases). For the 90% population, the model shows the peaks at 244356 (infected cases) and 9100 (death cases). Analysis revealed that the lockdown and recommended individual hygiene can slow down the outbreak but unable to eradicate the disease from the society. With the current infection and death rate and existing level of personal precautionary the number of infected individuals will be increasing.