In the past few years, unexpected natures of one of the best studied astronomical objects, Crab, were discovered. The energy spectrum of the Crab pulsar measured by Fermi LAT up to 30 GeV was consistent with the conventional theories predicting an exponential cutoff around a few GeV, while MAGIC measurements above 25 GeV and VERITAS measurements above 100 GeV revealed a surprising powerlaw- like tail up to 400 GeV, smoothly connected with Fermi LAT measurements.
On the other hand, the pulsar wind nebula of Crab, whose bright and steady emission have been used as a standard candle in many energy bands, showed a flaring activities in GeV band as detected by Fermi LAT and AGILE. MAGIC observed the Crab nebula during one of the GeV flares in April 2011, finding no significant flux enhancement above 700 GeV. Here we report on the details of the MAGIC observations of the Crab pulsar and nebula. For the pulsar, we also discuss the energy dependence of the pulse profile and theoretical interpretations of the power-law-like spectrum. For the nebula, in addition to the measurements during the GeV flare period, we discuss the average spectrum from 50 GeV to 45 TeV, which leads to precise determination of the IC peak combined with Fermi LAT measurements.