This article introduces Multivariate Modified Exponentially Weighted Moving Average (MMOEWMA) control chart, a chart for detecting shifts of all kinds in case of highly first order vector autoregressive VAR (1) process. This chart is based on modified MEWMA control chart statistic which is a correction of MEWMA chart statistic. The performance of MMOEWMA chart is illustrated along with MEWMA chart for a chemical process data. The average run length (ARL) properties of MMOEWMA scheme are derived using Markov Chain approach. Algorithm for the ARL computation and R-program of monitoring MMOEWMA control chart are provided.