Structural, magnetic and magnetocaloric properties of the Mn0.94Ti0.06CoGe alloy have been investigated using x-ray diffraction, DC magnetization and neutron diffraction measurements. Two phase transitions have been detected, at T-str = 235 K and T-C = 270 K. A giant magnetocaloric effect has been obtained at around Tstr associated with a structural phase transition from the low temperature orthorhombic TiNiSi-type structure to the high temperature hexagonal Ni2In-type structure, which is confirmed by neutron study. In the vicinity of the structural transition, at T-str, the magnetic entropy change, -Delta S-M reached a maximum value of 14.8 J kg(-1) K-1 under a magnetic field of 5 T, which is much higher than that previously reported for the parent compound MnCoGe. To investigate the nature of the magnetic phase transition around T-C = 270 K from the ferromagnetic to the paramagnetic state, we performed a detailed critical exponent study. The critical components gamma, beta and delta determined using the Kouvel-Fisher method, the modified Arrott plot and the critical isotherm analysis agree well. The values deduced for the critical exponents are close to the theoretical prediction from the mean-field model, indicating that the magnetic interactions are long range. On the basis of these critical exponents, the magnetization, field and temperature data around T-C collapse onto two curves obeying the single scaling equation M(H, epsilon) = epsilon(beta)f +/- (H/epsilon(beta+gamma)).