In mid-July, 1957, Miss Alice Bernard and her nieces, Bertha, Georgette, Blanche and Heloise LeBlanc donated to St. Peter's Parish, New Iberia, a tract of land containing ten acres on the Old Jeanerette Road on the outskirts of New Iberia. The donors hoped that the donated land would become at some point a new canonical parish. Nearly three years later, on June 25, 1960, the Feast of the Sacred Heart of Jesus, the wishes of the donors, together with the hopes and prayers of the Catholic community of New Iberia, were accorded when Bishop Maurice Schexnayder announced the creation of the new parish.

Carved out from the limits of St. Peter's Church, Our Lady of Perpetual Help Church in New Iberia and St. John's Church in Jeanerette, this tract of land among the cane fields along Bayou Teche has become Sacred Heart of Jesus Parish. Msgr. Curtis Vidrine served as its first pastor from 1960-1970. Succeeding him was Fr. T.J. Hebert 1970-1973, Msgr. Emery Labbe 1973-1974, Fr. J. Wilson Matt 1974-1996, Fr. Steve LeBlanc 1996-2007, Msgr. Richard Greene 2007-2016.  Father Michael Keith Landry became the new pastor in June 2016.

In December of 1996, Fr. Steve called together a building committee to begin looking into the growth and expansion of the parish as the current facilitites were quickly becoming inadequate for parish needs. Through a long process of surveying parish needs and intense planning, on Christmas of 2000, the parish celebrated its first liturgies in a new worship/gathering/education complex. The old church became a "new" parish hall, the rectory became an office building only, and the parish bought a residence in the neighborhood bordering church property as a residence for the pastor. The new parish complex was dedicated by Bishop Edward O'Donnell on June 20, 2001.

In 2010, a committee was formed to study the feasibility of renovating the 55 year old church building into a beautiful parish hall.  A successful capital campaign raised the funds for the renovation.  The good news was announced in April 2015 that approval of the contract was received from the Diocese and construction would begin in May 2015.  On March 1, 2016, the keys to the newly renovated parish hall were presented at the Parish Pastoral Council meeting. 

Sacred Heart of Jesus Catholic Church celebrated 60 years of being a church parish on June 25, 2020.