The paper deals with Dielectric Behaviour, Complex Impedance Spectroscopy and Magnetoelectric effect in La0.7Sr0.3MnO3(LSMO) and BaTiO3 (BT) Composites. The LSMO and BT are synthesized by hydroxide co-precipitation route. The nanocomposites are prepared by two series x LSMO + (1-x) BT + 2 wt % Bi2O3, for x = 0.05, 0.1, 0.15 and 0.2 ……series 1. x LSMO + (1-x) BT + 3 wt % Bi2O3, for x = 0.05, 0.1, 0.15 and 0.2 ……series 2. and sintered at Ts=1000°C and 1080°C. The composites are termed as LSMO-BT. The paper reports the crystal structure, micro-structural analysis, dielectric constant, complex impedance spectroscopy and magnetoelectric properties of LSMO-BT composites. It has been observed that the εr passes through a broad maximum at T ~ 124° C, which is nearly the ferroelectric transition temperature of BT. Both εr and εrmax increases as x increases from 0.05 to 0.2. The εr' and εr'' decreases sharply for all the compositions at low frequencies. This feature is typical of the presence of interfacial polarization. The variation of 4πMs is almost linear with x, the 4πMs increases with x as well as sintering aid. The 4πMs of respective compositions reduce as the sintering temperature is increased. The value of α increases for increase in sintering temperature as well as increase in wt % of the sintering aid. The magnitude of α is in the range as reported earlier for composites based on BT.