We report results of the first reverberation mapping campaign of I Zwicky 1 during $2014$-$2016$, which showed unambiguous reverberations of the broad H$beta$ line emission to the varying optical continuum. From analysis using several methods, we obtain a reverberation lag of $tau_{rm Hbeta}=37.2^{+4.5}_{-4.9},$ days. Taking a virial factor of $f_{_{rm BLR}}=1$, we find a black hole mass of $M_{bullet}=9.30_{-1.38}^{+1.26}times 10^6 M_{odot}$ from the mean spectra. The accretion rate is estimated to be $203.9_{-65.8}^{+61.0},L_{rm Edd}c^{-2}$, suggesting a super-Eddington accretor, where $L_{rm Edd}$ is the Eddington luminosity and $c$ is the speed of light. By decomposing {it Hubble Space Telescope} images, we find that the stellar mass of the bulge of its host galaxy is $log (M_{rm bulge}/M_{odot}) = rm 10.92pm 0.07$. This leads to a black hole to bulge mass ratio of $sim 10^{-4}$, which is significantly smaller than that of classical bulges and elliptical galaxies. After subtracting the host contamination from the observed luminosity, we find that I Zw 1 follows the empirical $R_{rm BLR}propto L_{5100}^{1/2}$ relation.
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