Indirect Matrix Converter (IMC) using two stages configuration is topologically more flexible than 3×3 Direct Matrix Converter (DMC). Due to the absence of passive components, the input and output terminals of matrix converters are coupled physically with the same instantaneous power. The output voltages are decided by the input grid voltages whereas the input currents are drawn from the load currents. This paper presents a carrier-based modulation strategy for IMC under unbalanced grid voltage conditions to produce high quality balanced output voltages and sinusoidal input currents without low order harmonics. Step-by-step implementations for the modulation schemes are explained in detail, inclusive of sequence components detection of grid voltages, modulation for current source rectifier (CSR), variable slope triangle carrier generation, online fictitious dc-link voltage calculations and modulation strategy for voltage source inverter (VSI) with compensated dc-link voltage. Theoretical analysis and mathematical proof for balanced outputs and sinusoidal inputs are provided to show validities of the proposed method. The maximum input-to-output voltage transfer ratio is found to be less than 0.866 and is highly related to the unbalance ratio and phase angle difference between positive and negative sequence grid voltages. Simulation and experimental results are provided to validate the effectiveness of the modulation schemes for IMC.